Find x. Round your answer to the nearest tenth of a degree.

Answer:

x < 11.5

Step-by-step explanation:

2x + 9 < 32

(2x + 9) - 9  < 32 - 9

2x < 23

2x/2 < 23/2

x < 11.5

Answer:

x < 11 1/2

Step-by-step explanation:

2x+9<32

Subtract 9 from each side

2x+9-9 < 32-9

2x<23

Divide by 2

2x/2 <23/2

x < 11 1/2

X is any number less than 11 1/2

Answer:

d.  a = 39

Step-by-step explanation:

Question:

for which value of "a" will the trinomial be factorizable.

x^2+ax-40

For the expression to have integer factors, a = sum of the pairs of factors of -40.

-40 has following pairs of factors

{(1,-40), (2,-20, (4,-10), (5,-8), (8, -5), (10,-4), (20,-2), (40,-1) }

meaning that the possible values of a are

+/- 39, +/- 18, +/- 6, +/- 3

out of which only +39 appears on answer d.  a=39

Answer:

-10, 40, -240, 1,920 and -19, 200

Step-by-step explanation:

Given the recurrence relation of the sequence defined as aₙ₊₁ = -2naₙ for n = 1, 2, 3... where a₁ = 5, to get the first five terms of the sequence, we will find the values for when n = 1 to n =5.

when n= 1;

aₙ₊₁ = -2naₙ

a₁₊₁ = -2(1)a₁

a₂ = -2(1)(5)

a₂ = -10

when n = 2;

a₂₊₁ = -2(2)a₂

a₃ = -2(2)(-10)

a₃ = 40

when n = 3;

a₃₊₁ = -2(3)a₃

a₄ = -2(3)(40)

a₄ = -240

when n= 4;

a₄₊₁ = -2(4)a₄

a₅ = -2(4)(-240)

a₅ = 1,920

when n = 5;

a₅₊₁ = -2(5)a₅

a₆ = -2(5)(1920)

a₆ = -19,200

Hence, the first five terms of the sequence is -10, 40, -240, 1,920 and -19, 200

Answer:

Step-by-step explanation:

The equivalent between sets is determined by the number of elements. If two sets have the same number of elements, then they are equivalent sets.

In this case, a year has 12 months, and the US has 50 states. So, one month is not equal to 1 state because they have different natures and they represent a different proportion. A month represents 1/12 of a year and a state represents 1/50 of the total number of states.

Step-by-step explanation:

given,

base( b) = 6cm

height (h)= 11cm

now, area of parallelogram (a)= b×h

or, a = 6cm ×11cm

therefore the area of parallelogram (p) is 66cm^2.

hope it helps...

The set of numbers that can represent the lengths of the sides of a triangle are 3,5,7. That is option B.

Triangle is defined as a type of polygon that has three sides in which the sum of both sides is greater than the third side.

That is to say, 3+5 = 8 is greater than the third side which is 7.

Therefore, the set of numbers the would represent a triangle are 3,5,7.

Learn more about triangle here:

https://brainly.com/question/17335144

#SPJ1

Answer:

0.07

Step-by-step explanation:

The number of sophmores is 2+25+3 = 30.

Of these sophmores, 2 drive to school.

So the probability that a student drives to school, given that they are a sophmore, is 2/30, or approximately 0.07.

Answer:

[tex]\large \boxed{0.07}[/tex]

Step-by-step explanation:

The usual question is, "What is the probability of A, given B?"

They are asking, "What is the probability that you are driving to school if you are a sophomore (rather than taking the bus or walking)?"

We must first complete your frequency table by calculating the totals for each row and column.

The table shows that there are 30 students, two of whom drive to school.

[tex]P = \dfrac{2}{30}= \mathbf{0.07}\\\\\text{The conditional probability is $\large \boxed{\mathbf{0.07}}$}[/tex]

Answer:

Step-by-step explanation:

Write in slope intercept form.

y - 9 = -2(x - 8)

y - 9 = -2x + 16

y = -2x + 16 + 9

y = -2x + 25

y = mx + b

The m is the slope, b is the y-intercept.

y = -2 x + 25

The slope is -2.

Answer:

16$

Step-by-step explanation:

8*2=16

HOPE THIS HELPS :)

Answer: $16

Step-by-step explanation:

As the book was purchased for half its price plus 8 you can create the equation 1/2x + 8 = x.  Then, simplifying the expression you get x = 16.  Thus, the book costs 16 dollars.

Answer:

.7698

Step-by-step explanation:

Answer:

2y (x^2+9) ( x-5)

Step-by-step explanation:

2x^3y + 18xy - 10x^2y - 90y

Factor out the common factor of 2y

2y(x^3+9x-5x^2-45)

Then factor by grouping

2y(x^3+9x     -5x^2-45)

Taking x from the first group and -5 from the second

2y( x (x^2+9)  -5(x^2+9))

Now factor out (x^2+9)

2y (x^2+9) ( x-5)

Answer:

[tex]3\frac{4}{5}[/tex]

Step-by-step explanation:

You first need to make the denominators the same and the LCM (least Common Multiple of this equation is 10.

10/10-->1

1/2--> 5/10

2--> 20/10

3/10, the denominator is already 10, so don't need to change.

10/10+5/10+20/10+3/10=38/10=[tex]3\frac{8}{10}[/tex]=[tex]3\frac{4}{5}[/tex]

Answer:

3 4/5

Step-by-step explanation:

hopefully this helped :3

Step-by-step explanation:

With the packaging of 8

48 cookies = 48 ÷ 8 = 6 boxes

With the packaging of 24

48 cookies = 48 ÷ 24 = 2 boxes

Answer:

[tex]n=(\frac{2.58(58.2)}{1})^2 =22546.82 \approx 22547[/tex]

So the answer for this case would be n=22547 rounded up to the nearest integer

Step-by-step explanation:

Let's define some notation

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

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

[tex]\sigma=58.2[/tex] represent the population standard deviation

n represent the sample size  

[tex] ME =1[/tex] represent the margin of error desire

The margin of error is given by this formula:

[tex] ME=z_{\alpha/2}\frac{\sigma}{\sqrt{n}}[/tex]    (a)

And on this case we have that ME =+1 and we are interested in order to find the value of n, if we solve n from equation (a) we got:

[tex]n=(\frac{z_{\alpha/2} \sigma}{ME})^2[/tex]   (b)

The critical value for 99% of confidence interval now can be founded using the normal distribution. The significance would be [tex]\alpha=0.01[/tex] and the critical value [tex]z_{\alpha/2}=2.58[/tex], replacing into formula (b) we got:

[tex]n=(\frac{2.58(58.2)}{1})^2 =22546.82 \approx 22547[/tex]

So the answer for this case would be n=22547 rounded up to the nearest integer

Answer:  width = 300

Step-by-step explanation:

Area (A) = Length (L) x width (w)

Given: A = 268,500

           L = 3w - 5

           w = w

268,500 = (3w - 5) x (w)

268,500 = 3w² - 5w

            0 = 3w² - 5w - 268,500

            0 = (3w + 895) (w - 300)

   0 = 3w + 895        0 = w - 300

  -985/3 = w             300 = w

Since width cannot be negative, disregard w = -985/3

So the only valid answer is: w = 300

Answer:

Side 1: 40 feet

Side 2: 20 feet

Side 3: 22 feet

Step-by-step explanation:

Side 1 is twice the length of side 2 and side 2 is 20 feet, which means side 1 is 40 feet. Side 3 is the the length of the second side plus 2, which means it has a length of 22 feet.

Answer:

rhombus

Step-by-step explanation:

on edge

Answer:

0.007

Step-by-step explanation:

We were told in the above question that a random sample of 51 households is monitored for one year to determine aluminum usage

Step 1

We would have to find the sample standard deviation.

We use the formula = σ/√n

σ = 12.2 pounds

n = number of house holds = 51

= 12.2/√51

Sample Standard deviation = 1.7083417025.

Step 2

We find the z score for when the sample mean is more than 61

z-score formula is z = (x-μ)/σ

where:

x = raw score = 61 pounds

μ = the population mean = 56.8 pounds

σ = the sample standard deviation = 1.7083417025

z = (x-μ)/σ

z = (61 - 56.8)/ 1.7083417025

z = 2.45852

Finding the Probability using the z score table

P(z = 2.45852) = 0.99302

P(x>61) = 1 - P(z = 2.45852) = 0.0069755

≈ 0.007

Therefore,the probability that the sample mean will be more than 61 pounds is 0.007

Answer:

(x + 8)² + (y - 3)² = 64

Step-by-step explanation:

The equation of a circle in standard form is

(x - h)² + (y - k)² = r²

where (h, k) are the coordinates of the centre and r is the radius

Here (h, k) = (- 8, 3) and r = 8 , thus

(x - (- 8))² + (y - 3)² = 8² , that is

(x + 8)² + (y - 3)² = 64

Answer:

See below.

Step-by-step explanation:

The equation for a circle is:

[tex](x-h)^2+(y-k)^2=r^2[/tex], where (h,k) is the center and r is the radius.

Plug in what we know. (-8,3) for (h,k) respectively and 8 for the radius:

[tex](x-(-8))^2+(y-(3))^2=(8)^2[/tex]

[tex](x+8)^2+(y-3)^2=64[/tex]

Answer:

Step-by-step explanation:

Least common denominator = a²b²

[tex]\frac{3}{a^{2}}+\frac{2}{ab^{2}}=\frac{3*b^{2}}{a^{2}*b^{2}}+\frac{2*a}{ab^{2}*a}\\\\=\frac{3b^{2}}{a^{2}b^{2}}+\frac{2a}{a^{2}b^{2}}\\\\=\frac{3b^{2}+2a}{a^{2}b^{2}}[/tex]

The discontinuity occurs when x is either -5 or 3.

That is determined by solving denominator = 0 quadratic equation for x.

Hope this helps.

Answer:

Step-by-step explanation:

Given the confidence interval of the heights of american heights given as (65.3,73.7);

Lower confidence interval L = 65.3 and Upper confidence interval U = 73.7

Sample mean will be the average of both confidence interval . This is expressed mathematically as [tex]\overline x = \frac{L+U}{2}[/tex]

[tex]\overline x = \frac{65.3+73.7}{2}\\\overline x = \frac{139}{2}\\\overline x = 69.5[/tex]

Hence, the sample mean is 69.5

Answers:

please see the attached picture for full solution..

Hope it helps....

Good luck on your assignment...

Answer:

k = -6

Step-by-step explanation:

hello

saying that (x-2) is a factor of [tex]x^2+x+k[/tex]

means that 2 is a zero of

[tex]x^2+x+k=0 \ so\\2^2+2+k=0\\<=> 4+2+k=0\\<=> 6+k =0\\<=> k = -6[/tex]

and we can verify as

[tex](x^2+x-6)=(x-2)(x+3)[/tex]

so it is all good

hope this helps

Answer:

Step-by-step explanation:

Length of an arc is expressed as [tex]L = \frac{\theta}{2\pi } * 2\pi r\\[/tex]. Given;

[tex]\theta = \frac{5\pi }{6} rad\\ radius = 24in\\[/tex]

The length of the minor arc SV is expressed as:

[tex]L = \frac{\frac{5\pi }{6} }{2\pi } * 2\pi (24)\\L = \frac{5\pi }{12\pi } * 48\pi \\L = \frac{5}{12} * 48\pi \\L = \frac{240\pi }{12} \\L = 20\pi \ in[/tex]

Hence, The length  of the arc SV is 20π in

Answer:

20 pi

Step-by-step explanation:

Answer:

[tex]\dfrac{dx}{dt}=-1.3846$ sales per day[/tex]

Step-by-step explanation:

The price​ p, in​ dollars, and the number of​ sales, x, of a certain item follow the equation: 6p+3x+2px=69

Taking the derivative of the equation with respect to time, we obtain:

[tex]6\dfrac{dp}{dt} +3\dfrac{dx}{dt}+2p\dfrac{dx}{dt}+2x\dfrac{dp}{dt}=0\\$Rearranging$\\6\dfrac{dp}{dt}+2x\dfrac{dp}{dt}+3\dfrac{dx}{dt}+2p\dfrac{dx}{dt}=0\\\\(6+2x)\dfrac{dp}{dt}+(3+2p)\dfrac{dx}{dt}=0[/tex]

When x=3, p=5 and [tex]\dfrac{dp}{dt}=1.5[/tex]

[tex](6+2(3))(1.5)+(3+2(5))\dfrac{dx}{dt}=0\\(6+6)(1.5)+(3+10)\dfrac{dx}{dt}=0\\18+13\dfrac{dx}{dt}=0\\13\dfrac{dx}{dt}=-18\\\dfrac{dx}{dt}=-\dfrac{18}{13}\\\\\dfrac{dx}{dt}=-1.3846$ sales per day[/tex]

The number of sales, x is decreasing at a rate of 1.3846 sales per day.

Answer:

see below

Step-by-step explanation:

Let x be the original price

x* discount rate = discount

x * 60% = 30

Change to decimal form

x * .60 = 30

Divide each side by .60

x = 30/.60

x =50

The original price was 50 dollars

Answer:

A-30     B-20    C-50

Step-by-step explanation:

Answer: MN represents the radius of the circle.

Step-by-step explanation:

The radius is the distance from the center to the outside of the circle.

The required 90% confidence interval for adult males is

[tex]\text {CI} = (64.2, \: 70.6)\\\\[/tex]

The required 90% confidence interval for adult females is

[tex]\text {CI} = (72, \: 79.2)\\\\[/tex]

The confidence interval of male and female pulse rates do not overlap since the mean pulse rate of female is way greater than the mean pulse rate of males.

Step-by-step explanation:

We are given the pulse rates of adult females and adult males and we have to construct the 90% confidence interval of the mean pulse rate for males and females.

Let us first compute the mean and standard deviation of the given pulse rates data.

Using Excel,  

=AVERAGE(number1, number2,....)  

The mean pulse rate of adult males is found to be

[tex]\bar{x}_{male} = 67.4[/tex]

The mean pulse rate of adult females is found to be

[tex]\bar{x}_{female} = 75.6[/tex]

Using Excel,  

=STDEV(number1, number2,....)    

The standard deviation for adult male pulse rate is found to be

 [tex]s_{male} = 11.9[/tex]

The standard deviation for adult female pulse rate is found to be  

 [tex]s_{female} = 13.5[/tex]

The confidence interval is given by

[tex]$ \text {CI} = \bar{x} \pm t_{\alpha/2}(\frac{s}{\sqrt{n} } ) $\\\\[/tex]

Where [tex]\bar{x}[/tex] is the sample mean, n is the sample size, s is the sample standard deviation and   [tex]t_{\alpha/2}[/tex] is the t-score corresponding to a 90% confidence level.  

The t-score corresponding to a 90% confidence level is  

Significance level = α = 1 - 0.90 = 0.10/2 = 0.05  

Degree of freedom = n - 1 = 40 - 1 = 39

From the t-table at α = 0.05 and DoF = 39

t-score =  1.685

The required 90% confidence interval for adult males is

[tex]\text {CI} = 67.4 \pm 1.685\cdot \frac{11.9}{\sqrt{40} } \\\\\text {CI} = 67.4 \pm 1.685\cdot 1.882\\\\\text {CI} = 67.4 \pm 3.17\\\\\text {CI} = 67.4 - 3.17, \: 67.4 + 3.17\\\\\text {CI} = (64.2, \: 70.6)\\\\[/tex]

Therefore, we are 90% confident that the actual mean pulse rate of adult male is within the range of 64.2 to 70.6 bpm

The required 90% confidence interval for adult females is

[tex]\text {CI} = 75.6 \pm 1.685\cdot \frac{13.5}{\sqrt{40} } \\\\\text {CI} = 75.6 \pm 1.685\cdot 2.1345\\\\\text {CI} = 75.6 \pm 3.60\\\\\text {CI} = 75.6 - 3.60, \: 75.6 + 3.60\\\\\text {CI} = (72, \: 79.2)\\\\[/tex]

Therefore, we are 90% confident that the actual mean pulse rate of adult female is within the range of 72 to 79.2 bpm

Comparison:

The confidence interval of male and female pulse rates do not overlap since the mean pulse rate of female is way greater than the mean pulse rate of males.

Answer:

No

Step-by-step explanation:

Let's check the first statement with an example. 2 and 3 are positive numbers and their sum (5) is also positive so his first statement is true.

To check the second statement let's look at the negative numbers -1 and -8 for example. Their sum (-9) is also negative so his second statement is true.

To check the third statement let's look at the numbers 9 and -5. One is positive and one is negative, but their sum (4) is positive, so his third statement is false. However if we look at the numbers 4 and -7, their sum is negative so the third statement is partially false.