Select the two values of x that are roots of this equation.
2x - 5 = -3x2
O A. X = 1
B. x= -1
C. X = 3
D. x =

Answer:

-2 < x < 35

Step-by-step explanation:

We have that the larger side has a larger opposite angle and the smaller sides and a smaller opposite angle.

The opposite angle of the 14 unit side is 37 °.

The opposite angle of the 13-unit side is (x + 2) °.

Since 13 <14, it would be:

x + 2 <37

we subtract 2 on both sides

x <35

The value of x must be less than 35.

Now, to form a triangle, the angle must be greater than 0.

x + 2> 0

we subtract 2 on both sides

x> -2

The value of x must be greater than - 2.

Therefore the answer would be:

-2 <x <35

Answer:

(CX3)+10

Step-by-step explanation:

Answer:

c×3+10= j

Step-by-step explanation:

Answer:

10

Step-by-step explanation:

for this you need to sub the value of -3 for x

Q(-3)=(-3)^2-(-3)-2

=9+3-2

=10

Answer:

Q= x - X/x - 2/x

Step-by-step explanation:

hope this helps !

Answer:

y=6x-13

Step-by-step explanation:

Since we are given a point and a slope, we can use the slope intercept formula.

[tex]y-y_{1} = m(x-x_{1} )[/tex]

where (x1, y1) is a point and m is the slope.

We know that the slope is 6 and the point is (3,5). Therefore,

x1= 3

y1= 5

m=6

Substitute these into the formula.

[tex]y-5 = 6(x-3 )[/tex]

Distribute the 6. Multiply each term inside the parentheses by the number outside the parentheses.

[tex]y-5= (6*x) + (6*-3)[/tex]

[tex]y-5=6x-18[/tex]

We want to find the slope-intercept form, or y=mx+b. Therefore, we must get y by itself.

5 is being subtracted from y. The inverse of subtraction is addition. Add 5 to both sides.

[tex]y-5+5=6x-18+5[/tex]

[tex]y= 6x-18+5[/tex]

[tex]y= 6x -13[/tex]

Answer:

P = 1/2

Step-by-step explanation:

If the tourist spends more than 275$, they must not arrive in Chicago by bus.

( 150 + 60 < 275, 150 + 40 < 275)

The total options the tourist can make:

3 x 2 = 6

(1st leg: 3 possible options, 2nd leg: 2 possible options)

The number of options the tourist can make after excluding bus option:

2 x 2 = 4

(1st leg: 2 remaining possible options, 2nd leg: 2 possible options)

The number of options the tourist can make after excluding the bus option and spend more than 275$:

4 - 1 = 3

(excluding the case of selecting train and cab, because 225 + 40 < 275)

=> The probability that the tourist will spend more than 275$ on these 2 legs of the trip:

P = 3/6 = 1/2

Probability helps us to know the chances of an event occurring. The probability that a tourist will spend more than $275 on these 2 legs of the trip is 0.5.

Probability helps us to know the chances of an event occurring.

[tex]\rm Probability=\dfrac{Desired\ Outcomes}{Total\ Number\ of\ outcomes\ possible}[/tex]

Given that Tourists have three choices for how to travel from New York to Chicago. They can take an aeroplane for $350, a bus for $150, or a train for $225. Also, when they arrive in Chicago, they can travel by van to their hotel for $60 or take a cab for $40. Therefore, the cost of different routes is,

As it can be seen that there are 3 cases where a tourist will spend more than $275, while the total number of cases is 6. Therefore, the probability that a tourist will spend more than $275 on these 2 legs of the trip is,

Probability = 3/6 = 1/2 =0.5z

Hence, the probability that a tourist will spend more than $275 on these 2 legs of the trip is 0.5.

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Answer:

It's written as

[tex]89.7 \times {10}^{9} [/tex]

Or

[tex]8.97 \times {10}^{10} [/tex]

Hope this helps you

Answer:

8.97 * 10 ^10

Step-by-step explanation:

We want one nonzero digit to the left of the decimal

8.97

We moved the decimal 10 places to the left

The exponent is positive 10 since we moved 10 places to the left

8.97 * 10 ^10

Answer:

(A)Only f(x) and h(x) have y-intercepts.

(C)The minimum of h(x) is less than the other minimums.

(E)The maximum of g(x) is greater than the other maximums.

Step-by-step explanation:

From the table

f(0)=0 and h(0)=0, therefore, Only f(x) and h(x) have y-intercepts. (Option A)

Therefore, the minimum of h(x) is less than the other minimums. (Option C).

Maximum of f(x)=14

Maximum of g(x)=49

Maximum of h(x)=0

Therefore, the maximum of g(x) is greater than the other maximums. (Option E)

Answer: It's B,C, and E

Step-by-step explanation:

Answer:

3

Step-by-step explanation:

Vlookup is a technique in excel which enables users to search for criterion values. It is vertical lookup function in excel which return a value from a different column. The formula for Vlookup function is:

=Vlookup'select cell you want to look up in' select cell you want to lookup from' select column index number' true/false.

where true is approximate match and false is exact match.

Answer:

P [ x > 59000} = 0,6057

Step-by-step explanation:

We assume Normal Distribution

P [ x > 59000} = (x - μ₀ ) /σ/√n

P [ x > 59000} =  (59000 - 60000)/ 3800

P [ x > 59000} = - 1000/3800/√35

P [ x > 59000} = - 1000*5,916 /3800

P [ x > 59000} =  - 5916/3800

P [ x > 59000} = - 1,55

We look for p value for that z score n z-table and find

P [ x > 59000} = 0,6057

Answer:

(a)[tex]D(x)=-2,500x+60,000[/tex]

(b)[tex]R(x)=60,000x-2500x^2[/tex]

(c) x=12

(d)Optimal ticket price: $12

Maximum Revenue:$360,000

Step-by-step explanation:

The stadium holds up to 50,000 spectators.

When ticket prices were set at $12, the average attendance was 30,000.

When the ticket prices were on sale for $10, the average attendance was 35,000.

(a)The number of people that will buy tickets when they are priced at x dollars per ticket = D(x)

Since D(x) is a linear function of the form y=mx+b, we first find the slope using the points (12,30000) and (10,35000).

[tex]\text{Slope, m}=\dfrac{30000-35000}{12-10}=-2500[/tex]

Therefore, we have:

[tex]y=-2500x+b[/tex]

At point (12,30000)

[tex]30000=-2500(12)+b\\b=30000+30000\\b=60000[/tex]

Therefore:

[tex]D(x)=-2,500x+60,000[/tex]

(b)Revenue

[tex]R(x)=x \cdot D(x) \implies R(x)=x(-2,500x+60,000)\\\\R(x)=60,000x-2500x^2[/tex]

(c)To find the critical values for R(x), we take the derivative and solve by setting it equal to zero.

[tex]R(x)=60,000x-2500x^2\\R'(x)=60,000-5,000x\\60,000-5,000x=0\\60,000=5,000x\\x=12[/tex]

The critical value of R(x) is x=12.

(d)If the possible range of ticket prices (in dollars) is given by the interval [1,24]

Using the closed interval method, we evaluate R(x) at x=1, 12 and 24.

[tex]R(x)=60,000x-2500x^2\\R(1)=60,000(1)-2500(1)^2=\$57,500\\R(12)=60,000(12)-2500(12)^2=\$360,000\\R(24)=60,000(24)-2500(24)^2=\$0[/tex]

Therefore:

Answer:

Step-by-step explanation:

[tex]7^{0}=1[/tex]

[tex](7^{13})^{3}*7^{0}=7^{13*3}*1\\\\=7^{39}[/tex]

Answer:

D. 3 and -4

Step-by-step explanation:

Given the expression, x² - x - 12, let's factorise to find the value of p and q using the table, for which we would have the expression simplified as (x + p)(x + q)

From the table, let's find the values of p and q that would give us -12 when multiplied together, and would also give us -1 when summed together.

Thus, from the table given, the row containing the values of p(3) and q(-4) gives us = -1 (p+q) . p = 3, q = -4 would be our values to use to factor x² - x - 12, as multiplying both will also give us "-12".

Thus, x² - x - 12 would be factorised or simplified as (x + 3)(x - 4)

Therefore, the answer is: D. 3 and -4

Answer:

D a p e x

Step-by-step explanation:

Answer:

48

Step-by-step explanation:

You are doubling 2 dimensions, so you just multiply the volume by 2 each time. Since you are doing it twice, you multiply the volume by 4. 12*4=48. You could also brute force it and just do 24*36*12/216(the volume of the 6 inch cube).

Given that, a box in the shape of a rectangular prism, with dimensions 12 inches by 18 inches by 12 inches, can hold exactly 12 cubes measuring 6 inches on each side.

We need to find that how many cubes it holds if the length and width of the base are doubled,

We know that,

Volume of a rectangular prism = length × width × height

Volume of the new rectangular prism, = 2length × 2width × height

= 4(length × width × height)

= 4(12·12·18)

= 4×2592

= 10,368

Volume of the cube = side³

= 6³ = 216

The number of cube that the new rectangular prism can hold = Volume of the rectangular prism / Volume of the cube

= 10,368 / 216

= 48

Hence, the new rectangular prism, can hold 48 cubes.

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Answer:

A 90% confidence interval for the standard deviation of the fracture toughness distribution is [4.06, 6.82].

Step-by-step explanation:

We are given the following observations that were made on fracture toughness of a base plate of 18% nickel maraging steel below;

68.6, 71.9, 72.6, 73.1, 73.3, 73.5, 75.5, 75.7, 75.8, 76.1, 76.2,  76.2, 77.0, 77.9, 78.1, 79.6, 79.8, 79.9, 80.1, 82.2, 83.7, 93.4.

Firstly, the pivotal quantity for finding the confidence interval for the standard deviation is given by;

                             P.Q.  =  [tex]\frac{(n-1) \times s^{2} }{\sigma^{2} }[/tex]  ~ [tex]\chi^{2} __n_-_1[/tex]

where, s = sample standard deviation = [tex]\sqrt{\frac{\sum (X - \bar X^{2}) }{n-1} }[/tex] = 5.063

            [tex]\sigma[/tex] = population standard deviation

            n = sample of observations = 22

Here for constructing a 90% confidence interval we have used One-sample chi-square test statistics.

So, 90% confidence interval for the population standard deviation, [tex]\sigma[/tex] is ;

P(11.59 < [tex]\chi^{2}__2_1[/tex] < 32.67) = 0.90  {As the critical value of chi at 21 degrees  

                                                  of freedom are 11.59 & 32.67}  

P(11.59 < [tex]\frac{(n-1) \times s^{2} }{\sigma^{2} }[/tex] < 32.67) = 0.90

P( [tex]\frac{ 11.59}{(n-1) \times s^{2}}[/tex] < [tex]\frac{1}{\sigma^{2} }[/tex] < [tex]\frac{ 32.67}{(n-1) \times s^{2}}[/tex] ) = 0.90

P( [tex]\frac{(n-1) \times s^{2} }{32.67 }[/tex] < [tex]\sigma^{2}[/tex] < [tex]\frac{(n-1) \times s^{2} }{11.59 }[/tex] ) = 0.90

90% confidence interval for [tex]\sigma^{2}[/tex] = [ [tex]\frac{(n-1) \times s^{2} }{32.67 }[/tex] , [tex]\frac{(n-1) \times s^{2} }{11.59 }[/tex] ]

                                     = [ [tex]\frac{21 \times 5.063^{2} }{32.67 }[/tex] , [tex]\frac{21 \times 5.063^{2} }{11.59 }[/tex] ]

                                     = [16.48 , 46.45]

90% confidence interval for [tex]\sigma[/tex] = [[tex]\sqrt{16.48}[/tex] , [tex]\sqrt{46.45}[/tex] ]

                                                 = [4.06 , 6.82]

Therefore, a 90% confidence interval for the standard deviation of the fracture toughness distribution is [4.06, 6.82].

Answer:

Step-by-step explanation:

Using the alternative hypothesis (µ < µ0),

To find the p-value with test statistic -1.25 and assuming a standard level of significance of 0.05, using a p value calculator, the p-value is 0.1057 which is great that 0.05. Thus, the results is not significant.

Using the p value calculation.

1. Check the left tailed z table as the test statistic is negative,

2. Then find the probabilitythat z is greater than your test statistic (look up your test statistic on the z-table- the value under 1.2 and 0.05 which is 0.8944

3. Then, find its corresponding probability, and subtract it from 1 to get your p-value- 1-0.8944 = 0.1056.

Answer:

The null and alternative hypothesis can be written as:

[tex]H_0: \pi_1-\pi_2=0\\\\H_a:\pi_1-\pi_2< 0[/tex]

Step-by-step explanation:

This is a hypothesis test for the difference between proportions.

The claim is that the proportion of 18- to 34-year-old Americans that own a cell phone is less than the proportion of 35- to 49-year-old Americans.

This claim will be reflected in the alternnative hypothesis, that will state that the population proportion 1 (18 to 34) is significantly smaller than the population proportion 2 (35 to 49).

On the contrary, the null hypothesis will state that the population proportion 1 is ot significantly smaller than the population proportion 2.

Then, the null and alternative hypothesis can be written as:

[tex]H_0: \pi_1-\pi_2=0\\\\H_a:\pi_1-\pi_2< 0[/tex]

The significance level is assumed to be 0.05.

The sample 1, of size n1=200 has a proportion of p1=0.63.

[tex]p_1=X_1/n_1=126/200=0.63[/tex]

The sample 2, of size n2=175 has a proportion of p2=0.68.

[tex]p_2=X_2/n_2=119/175=0.68[/tex]

The difference between proportions is (p1-p2)=-0.05.

[tex]p_d=p_1-p_2=0.63-0.68=-0.05[/tex]

The pooled proportion, needed to calculate the standard error, is:

[tex]p=\dfrac{X_1+X_2}{n_1+n_2}=\dfrac{126+119}{200+175}=\dfrac{245}{375}=0.653[/tex]

The estimated standard error of the difference between means is computed using the formula:

[tex]s_{p1-p2}=\sqrt{\dfrac{p(1-p)}{n_1}+\dfrac{p(1-p)}{n_2}}=\sqrt{\dfrac{0.653*0.347}{200}+\dfrac{0.653*0.347}{175}}\\\\\\s_{p1-p2}=\sqrt{0.001132+0.001294}=\sqrt{0.002427}=0.049[/tex]

Then, we can calculate the z-statistic as:

[tex]z=\dfrac{p_d-(\pi_1-\pi_2)}{s_{p1-p2}}=\dfrac{-0.05-0}{0.049}=\dfrac{-0.05}{0.049}=-1.01[/tex]

This test is a left-tailed test, so the P-value for this test is calculated as (using a z-table):

[tex]\text{P-value}=P(z<-1.01)=0.1554[/tex]

As the P-value (0.1554) is bigger than the significance level (0.05), the effect is not significant.

The null hypothesis failed to be rejected.

There is not enough evidence to support the claim that the proportion of 18- to 34-year-old Americans that own a cell phone is less than the proportion of 35- to 49-year-old Americans.

Answer:

C

Step-by-step explanation:

We know that A is not true because we know that h(8) is 19, not 21. B is also not true because the value of h(x) can't be -1. D can't be true because x can't be 13, therefore the answer is C.

Answer:

There is not enough evidence to support the claim that women who exercise daily have a significantly different duration of labor than all women.

Standard error sm = 1.634

Test statistic t = 1.102

P-value = 0.28

Step-by-step explanation:

This is a hypothesis test for the population mean.

The claim is that women who exercise daily have a significantly different duration of labor than all women.

Then, the null and alternative hypothesis are:

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

The significance level is 0.05.

The sample has a size n=29.

The sample mean is M=17.8.

As the standard deviation of the population is not known, we estimate it with the sample standard deviation, that has a value of s=√77.4=8.8.

The estimated standard error of the mean is computed using the formula:

[tex]s_M=\dfrac{s}{\sqrt{n}}=\dfrac{8.8}{\sqrt{29}}=1.634[/tex]

Then, we can calculate the t-statistic as:

[tex]t=\dfrac{M-\mu}{s/\sqrt{n}}=\dfrac{17.8-16}{1.634}=\dfrac{1.8}{1.634}=1.102[/tex]

The degrees of freedom for this sample size are:

[tex]df=n-1=29-1=28[/tex]

This test is a two-tailed test, with 28 degrees of freedom and t=1.102, so the P-value for this test is calculated as (using a t-table):

[tex]\text{P-value}=2\cdot P(t>1.102)=0.28[/tex]

As the P-value (0.28) is bigger than the significance level (0.05), the effect is not significant.

The null hypothesis failed to be rejected.

There is not enough evidence to support the claim that women who exercise daily have a significantly different duration of labor than all women.

Answer:

x=9,3

Step-by-step explanation:

x²-12x=-27

x²-12x+(12/2)²=-27+(12/2)²

x²-12x+6²=-27+36

(x-6)²=9

x-6=[tex] \frac{ + }{ - } \sqrt{9} [/tex]

x-6=+3 and x-6=-3

x=9 and 3

Answer:

the correct answer is 2x

Answer:

D. 2x

Step-by-step explanation:

20x² : 1, 2, 4, 5, 10, 20, x

14x : 1, 2, 7, 14, x

The greatest common factor of the polynomial is 2x.

2x(10x² - 7)

Answer:

12x/2 or 52/2

Step-by-step explanation:

Ok, perimeter is length+length+width+width. 12x/2 and 52/2 could are probably the answers.

Answer:

Set 1: 30, 35, 32, 30, 29

Step-by-step explanation:

Let's first clarify what is accurate and precise:

Precise is based on how close two or more measured values are to each other. While something is said to be accurate, when the standard value values are close, which in our case is 30.

Therefore, we analyze each set:

Set 1: 30, 35, 32, 30, 29

This set is precise and accurate, since 2 values are 30 and all their values are close to each other.

Set 2: 15, 16, 12, 15, 14

This set is precise, because all of its values are close but not accurate.

Set 3: 19, 30, 78, 43, 30

This set is somewhat accurate because there are 2 values of 30, but it is not precise because its values are separate.

Set 4: 30, 30, 67, 12, 90

It is the same case of Set 3.

Therefore the answer is Set 1.

Answer:

Set 1: 30, 35, 32, 30, 29

Step-by-step explanation:

Answer:

657.96

Step-by-step explanation:

use formula A=P(1+r/n)^nt

A=500(1+.04/1)^1*7

A=500(1.04)^7

A=500(1.3159~)

A= 657.96~

Answer:

  no; 12

Step-by-step explanation:

A number divisible by 4 and 6 will be divisible by their least common multiple, 12. If it is an odd multiple of 12, it will not be divisible by 24.

Examples:

  12÷4 = 3; 12÷6 = 2; 12 is not divisible by 24

  24÷4 = 6; 24÷6 = 4; 24 is divisible by 24

  36÷4 = 9; 36÷6 = 6; 36 is not divisible by 24

Answer:

The area of the sheet is approximately 50.59 m² or 50.6 m²

Step-by-step explanation:

The area of a rectangle is given by the following expression:

[tex]area = width*height[/tex]

Since breadth is the same as the width of the sheet, we can calculate its area as shown below:

[tex]area = 9.96*5.08 = 50.59[/tex]

The area of the sheet is approximately 50.59 m² or 50.6 m²

Answer:

(-0.5, 0)

Step-by-step explanation:

Coordinates of endpoints of segment are:

A= (-2, 1)

B= (1, - 1)

By mid-point formula:

The midpoint of [tex] \overline{AB} [/tex]

[tex] = \bigg(\frac{ - 2 + 1}{2}, \: \: \frac{1 + ( - 1)}{2} \bigg) \\ \\ = \bigg(\frac{ - 1}{2}, \: \: \frac{0}{2} \bigg)\\ \\ = \bigg(\frac{ - 1}{2}, \: \: 0 \bigg)\\ \\ = ( - 0.5, \: \: 0 )[/tex]

Answer: See bolded below

Step-by-step explanation:

With the given f(x) and g(x) given, we can directly plug them in to solve. The inverse is to replace the y with x and x with y, then solve for y.

A. f(g(-4))=143

g(-4)=3(-4)+1

g(-4)=-12+1

g(-4)=-11

With g(-4), we plug that into f(x) to find f(g(-4)).

f(-11)=(-11)²-2(-11)

f(-11)=121+22

f(-11)=143

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

B. 9x²-1

(3x+1)²-2(3x+1)

(9x²+6x+1)-6x-2

9x²-1

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

C. g⁻¹(x)=(x-1)/3

x=3y+1

x-1=3y

(x-1)/3=y

Answer:

no solution

Step-by-step explanation:

4x+3y = 6

8x + 6y = 5

Multiply the first equation by -2

-2(4x+3y) = 6*-2

-8x -6y = -12

Add this to the second equation

-8x-6y = -12

8x + 6y = 5

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

0x + 0y = -7

0 = -7

Since this is never true there is no solution

Answer:

X = 8/3, y= -14/9

Step-by-step explanation:

using elimination method:

subtract equation 1 from equation 2

8x-4x + 6y-3y = 5-6

4x+3y= -1

4x= -1-3y

divide both sides by 4

x = -1-3y÷4

substitute x = -1-3y/4 in equation 2

8(-1-3y)/4 +6y = 5

-8-24y/4+ 6y =5

-8-24y+6y/4 =5

-8-18y/4 = 5

Cross multy

-8-18y × 1 = 4×5

-8-18y = 20

collect like terms

-18y = 20+8

-18y = 28

divide both sides by-18

y = 28/-8

y = -14/9

put y = -14/9 in equation 1

4x+3(-14/9) = 6

4x-42/9 = 6

42/9 = 14/3

so, 4x=6+14/3

LCM =3

4x = 18+14/3

4x= 32/3

cross multiply

4x×3 = 32

12x = 32

divide both sides by 12

12x/12= 32/12

x = 8/3

so, x = 8/3, y = -14/9

check:

first equation:

4(8/3) + 3(-14/9)

32/3 - 14/3( 3 cancels 9 rem 3)

LCM= 3

32 - 14/3

= 18/3

= 6

Answer:

P ≈ 317.08 m

Step-by-step explanation:

Circumference: C = πd

Step 1: Find circumference of both domes

C = π(50)

Since it's a dome, we divide by 2

50π/2 = 25π

Since we have 2 domes, we simply multiply by 2 again

25π(2) = 50π

Step 2: Find perimeter of track

50π + 80(2)

P = 50π + 160

P = 317.08 m

Answer and Step-by-step explanation:

The computation is shown below:

a. The economic order quantity is

[tex]= \sqrt{\frac{2\times \text{Annual demand}\times \text{Ordering cost}}{\text{Carrying cost}}}[/tex]

[tex]= \sqrt{\frac{2\times \text{6,100}\times \text{\$31}}{\text{\$8}}}[/tex]

= 217 units

b. The average inventory used is

[tex]= \frac{economic\ order\ quantity}{2}[/tex]

[tex]= \frac{217}{2}[/tex]

= 108.5 units

c. The optimal order per year

[tex]= \frac{annual\ demand}{economic\ order\ quantity}[/tex]

[tex]= \frac{6,100}{217}[/tex]

= 28 orders

d. The optima number of days is

[tex]= \frac{working\ days}{optimal\ number\ of\ orders}[/tex]

[tex]= \frac{250}{28}[/tex]

= 8.9 days

e. The total annual inventory cost is

= Purchase cost + ordering cost + carrying cost

where,

Purchase cost is

[tex]= \$6,100 \times \$101[/tex]

= $616,100

Ordering cost = Number of orders × ordering cost per order

= 28 orders × $31

= $868

Carrying cost = average inventory × carrying cost per unit

= 108.50 units × $8

= $868

So, the total would be  

= $616,100 + $868 + $868

= $617,836