Conjecture: How many solutions do x3 - 5x2 + 28 = 0 have? Find the real solution(s) of the equation. Then use polynomial long division to find the other solution(s).

Answer:

$233.39

Step-by-step explanation:

Pants = $82, 2 Shirts = $53 * 2, Shoes = $120

Add all these values up to find the total cost of your order excluding tax.

82 + 53(2) + 120 = 308

Next find the price w/ tax. Multiply 308 by 8.25%, or 0.0825.

308 * 0.0825 = 25.41

Now you add the tax to the total value.

308 + 25.41 = 333.41

The total value including tax is $333.41. The online retailer is offering a 30% savings (discount), so multiply the total price including tax by 30% (0.30).

333.41 * 0.30 = 100.023

Now you subtract the discount from the total price.

333.41 - 100.023 = 233.38700

The question say the answer rounded to the nearest cent or hundredths, so your final answer is 233.39.

The final price of the clothing including all discounts and taxes is $233.39.

Answer:

A. H: mu1< mu2

Step-by-step explanation:

Given that :

Mean amount of time per domestic cars = mu1

Mean amount of time per foreign cars = mu2

Automobile technicians claim :

The mean amount of time (in hours) per domestic car repair is more than that of foreign cars. This will be the Null hypothesis.

Null hypothesis : mu1 > mu2

The alternative hypothesis will negate the Null hypothesis and will hence be the opposite. This can this be expressed as :

Alternative hypothesis : mu1 < mu2

Answer:

8+7=15 therefore 8

                          5

Step-by-step explanation:

The numerator from the fraction of apple fruits to total fruits is 8

How to find fraction of apples to total fruits?

Total fruits = apples + oranges

= 8 + 7

= 15

Fraction of apple fruits to total fruits = Number of apples / Total fruits

= 8/15

Therefore, the numerator from the fraction of apple fruits to total fruits is 8

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Answer: 45 45 90

Step-by-step explanation:

Answer:

The rate of the heat flow = 1260 π

Step-by-step explanation:

From the information given :

k = 4.5

u(x,y,z) = 5y² + 5z²

Surface cylinder:

y² +z² = 5,     0 ≤ x ≤ 2

[tex]\mathtt{\overline F = \bigtriangledown u = -k(0,10y, 10z )}[/tex]

[tex]\mathtt{\overline F = -4.5(0,10y, 10z )}[/tex]

[tex]\mathtt{\overline F = (0,-45y, -45z ) \ --- (1)}[/tex]

Now parameterizing the surface by :

x = u  , y = [tex]\mathtt{\sqrt{7} \ cos \ t}[/tex]  , z = [tex]\mathtt{\sqrt{7} \ sin \ t}[/tex]

0 ≤ x ≤ 2        ,        0 ≤ t ≤ 2π

[tex]\mathtt{{ \left. \begin{array}{1} \overline{r_y} = (1,0,0) } \\ \\ \overline{r_t} = (0, \ - \sqrt{7}\ sin \ t, \sqrt{7} \ cos \ t) \end{array} \right\} = r_u \times r_t}[/tex]

[tex]\mathtt{\overline r_u \times \overline r_t = ( -0, - \sqrt{7} \ cos \ t , - \sqrt{7} \ sin \ t) --- (2)}[/tex]

Taking integral of both equations; we have:

[tex]\mathtt{= \int ^{2}_0 \int ^{2 \pi}_{0} (0, -45y, -45 z) (0, - \sqrt{7} \ cos \ t, - \sqrt{7} \ sin \ t) \ dtdu}[/tex]

[tex]\mathtt{= \int ^{2}_0 \int ^{2 \pi}_{0} ( 45\sqrt{7} \ y\ cos \ t+ 45 \sqrt{7} \ z \ sin \ t) \ dtdu}[/tex]

[tex]\mathtt{= 45\sqrt{7}\ \int ^{2}_0 \int ^{2 \pi}_{0} (( \sqrt{7} \ cos \ t)cos \ t + (\sqrt{7} \ \ sin \ t) sin \ t) \ dtdu}[/tex]

[tex]\mathtt{= 45\times {7}\ \int ^{2}_0 \int ^{2 \pi}_{0} (1) \ dtdu}[/tex]

= 315 × (2) × (2π)

= 1260 π

Answer:

See below for answers to both questions.

Step-by-step explanation:

Question 13)

We know that the perimeter is the sum of all of the side lengths of the square, and we know that a square has 4 sides that are all the same length.  This lets us set up the following equation:

4(10x + 6) = 74

To solve this equation, we should first distribute the 4 through the parentheses using the distributive property.

40x + 24 = 74

Next, we should subtract 24 from both sides of the equation.

40x = 50

Finally, we should divide both sides by 40.

x = 50/40 = 1.25

Therefore, the answer to question 13 is x = 1.25.

Question 14)

If we know the rectangle and triangle have the same perimeter, we can set up the following equation:

2(4x-1) + 2(x-1) = (4x + 1) + (3x + 5) + (x + 1)

We should begin by simplifying the left side of the equation using the distributive property, as we did above.

8x - 2 + 2x -2 = 4x + 1 + 3x + 5 + x + 1

Next, we can combine like terms on both sides of the equation.  This means adding together the constant terms (numbers) and also combining the variable terms (x's).  This is modeled below:

(8x + 2x) + (-2 + -2) = (4x + 3x + x) + (1 + 5 + 1)

10x - 4 = 8x + 7

Next, we should subtract 8x from both sides.

10x - 8x - 4 = 8x - 8x + 7

2x - 4 = 7

Next, we should add 4 to both sides.

2x - 4 + 4 = 7 +4

2x = 11

Finally, we should divide both sides by 2.

x = 11/2 = 5.5

The question asks us to find the perimeter, so we can use the perimeter of the rectangle:

10x - 4 = 10(5.5) - 4 = 51

Therefore, the answer is 51 units.

Hope this helps!

Answer:

B

Step-by-step explanation:

If the figure is regular, then everyone of the central angles are equal. They add up to 360 degrees.

x + x + x + x + x + x + x = 360          Combine

7x = 360                                           Divide by 7

x = 360/7

x = 51.43

Answer:

the answer is -7

Step-by-step explanation:

m+9=2-9

-9

m=. -7

Answer:

£837.5

Step-by-step explanation:

Cost of slabs =  £16.75 / m²

Ordered amount = 50 m²

Total cost:

Total cost of slabs is  £837.5

Answer:

The remainder is 87.

Step-by-step explanation:

By definition of remainder theorem, whenever a polynomial f(x) is divided by (x-b) the remainder will be: f(b)

Following the Remainder Theorem, in this question the remainder will be f(5).

In this case we were given f(x) as

f(x) = x^2 + 14x − 8

We're are to find the remainder when it is divided by (x-5)

Then(x-5)= 0

X=5

If we substitute x=5 into equation of f(x), we will have the remainder of

f(x) = x^2 + 14x − 8

f(4)= (5)^2 +14(5)-8

f(4)=25+70-8

f(4)=87

Hence, The remainder is 87.

Answer:

87

Step-by-step explanation:

Answer:

Accept the null hypothesis if it is two tailed test.

Step-by-step explanation:

The null hypotheses can only be accepted if it is a two tailed test and calculated chi square must be less than the critical value of chi square.

Then the difference between the  the observed and expected frequencies will be zero.

where

H0 : σ²-σ²= 0             Ha: σ²-σ²≠0

For this the critical region would be greater than the calculated value of chi square. If so we will accept the null hypothesis and reject the alternative hypothesis.

Answer:

4y²-7y+16yz+28z

Step-by-step explanation:

4y²-7y+16yz+28z

Answer:

the absolute value of -5 is 5, and the absolute value of 5 is also 5. ∣ a + b i ∣ = a 2 + b 2 . |a+bi| = \sqrt{a^2 +b^2}

please give me heart

Answer:

Yes

Step-by-step explanation:

Yes.  They did exponents and grouping symbols first, then multiplication and division left to right.  Addition came before multiplication and division because it was inside a grouping symbol.

Answer:

B

Step-by-step explanation:

∠ U = ∠ F = 76° thus are congruent

Consider the ratios of corresponding sides

[tex]\frac{UW}{FH}[/tex] = [tex]\frac{9}{21}[/tex] = [tex]\frac{3}{7}[/tex]

[tex]\frac{UV}{FG}[/tex] = [tex]\frac{18}{42}[/tex] = [tex]\frac{3}{7}[/tex]

Thus Δ UVW ~ Δ FGH by the SAS postulate

Yes the given two triangles are similar.

The similarity statement is B) ΔUVW ∼ ΔFGH

The triangles that have similar shape but the sizes of the triangles may be different, are called similar triangles.

Here, in the given triangles,

∠U = ∠F = 76°

Therefore they are congruent.

The ratio of corresponding sides, [tex]\frac{UW}{FH} =\frac{9}{21} = \frac{3}{7}[/tex]

Again the ratio of corresponding sides, [tex]\frac{UV}{FG}=\frac{18}{42}=\frac{3}{7}[/tex]

Thus, ΔUVW ∼ ΔFGH by SAS rule of similarity.

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Answer:

Debbie would need to purchase 2 1-gallon bottles of juice.

Step-by-step explanation:

So we have 20 cups and each cup holds 10 fluid ounces. 20 times 10 equals 200 fluid ounces. We need to see how many fluid ounces are in 1 gallon. There are 128 fluid ounces in 1 gallon. 200 divided by 128 equals to 1.56 gallons. Debbie needs more than 1 gallon. Since we have a decimal and 1 is on the left of the decimal, Debbie would need to purchase 2 1-gallon bottles of juice.

Answer:

d) r = -65.

Step-by-step explanation:

The absolute value of r represents the relationship strength and the sign represents the relationship direction

Also if the relationship is nearest to 1 then it would be termed as positive correlated and if the relationship is nearest to -1 then it would be termed as negative correlated

Therefore based on the given options, the last option is correct

Answer:

Y= 7.9 lb

X= 10.1 lb

Step-by-step explanation:

The chef orders 2.2 lb more carrots than celery. The two orders weigh 10.8 lb combined.

Let carrot= x

Let celery= y

X+y = 18...... equation one

X= 2.2 +y.... equation two

Substituting the value of x into equation one

2.2 +y +y =18

2y= 18-2.2

2y= 15.8

Y= 7.9 lb

Substituting the value of yinto equation 2

X= 2.2 +y

X= 2.2 + 7.9

X= 10.1 lb

Answer:

b= - 1.26317

a = 17.237

b. The selling price (in dollars) of a 7-year-old car

y =  8394.81 dollars

C.  For each additional year, the car decreases $ ___ in value.

1263.17 $ decreases per year

Step-by-step explanation:

Let y be the selling price in thousands and x be the age in years

Car         Age        Selling Price

             (years)           ($000)             XY                    X²  

                    X                 Y          

1                   9                  11.1              99.9                   81          

2                  5                  9.5              47.5                   25

3                 13                  4.4               57.2                 169

4                 17                  4.4               74.8                 289

5                 7                 8.06             56.42                49

6                1                   2.07            2.07                     1

7                  1                    0.6            0.6                      1

8                 14                  8.1              113.4                  196

9                12                   8.1              97.2                  144

10              17                    4.8             81.6                  289

11               4                     12.5           50                     16

12              4                      10.7            42.8                 16      

∑               97                    84.33          723.49            1276                

The estimated regression line of Y on X is

Y= a +bX

and the two normal equations are

∑ y= na + b∑X

∑XY= a∑X + b∑X²

Now

X`= ∑X/n = 97/12= 8.083

b= n∑XY - (∑X)(∑Y)/ n∑ X²- (∑X)²

b= 723.49 - (97)(84.33)/ 12(1276) - (97)²

b= -7456.52/ 5903

b= - 1.26317

a= Y`- b X`

a= 7.0275 - (-- 1.26317)8.083

a = 17.237

Y = 17.237  - 1.26317 X

y= - 1.26317 X + 17.237

b. The selling price (in dollars) of a 7-year-old car

y = - 1.26317 (7) + 17.237

y= 8.39481

y =  8394.81 dollars

C.  For each additional year, the car decreases $ ___ in value.

1.26317 *1000= 1263.17 $ decreases per year

Answer:

It will be 1:50

Step-by-step explanation:

Answer:

11:50 + 2 hr. = 1:50 or 13:50 Military/European time

Step-by-step explanation:

Answer:

Hey there!

In this expression, 5k and -6 are terms, not factors.

In this expression, 5 and k are factors, so the last option is correct.

Let me know if this helps :)

Answer:

5 and k are factors.

Step-by-step explanation:

A factor would be a value or variable which is multiplied by something else. It is 'a part' of the product.

In [tex]5k-6[/tex], 5 and k are being multiplied by each other. This would mean that 5 and k are factors.

Option E should be the correct answer.

Answer: Hi!

The place value of 6 in 37651 is equal to 600, as it is in the hundreds place.

All we need to do is multiply 600 by 11:

600 * 11 = 6600

Hope this helps!

━━━━━━━━━━━━━━━ ♡ ━━━━━━━━━━━━━━━  

So in 37,651, the 6 is in the hundreds place since it's the third digit (from right to left).

6 in the hundreds place is 600.

600 times 11 equals 6600.

━━━━━━━━━━━━━━━ ♡ ━━━━━━━━━━━━━━━  

♡ Hope this helps! ♡

❀ 0ranges ❀

Answer:

Step-by-step explanation:

In a single - sampling plan, when a decision on acceptance / rejection of the lot  is made on the basis of  only one sample, Then , the acceptance plan is said to be a single sampling plan. The single sampling plan is known as the most common and easiest sampling plan

The following symbol representation can be written as follows:

a. N    →   Lot size   from which the sample is drawn

b. n    →    sample size

c. c    →     acceptance number

d. d   →    number of defectives in the sample

For example:

if we take a  randomized sample of  size 'n' from the Lot size.

The next step will be to inspect all items in the sample to find the defectives 'd'

The decision rule is that:

If  the number of defectives is less than or equal to acceptance number, then answer is YES i.e d ≤ c, Then ,  we accept the Lot

If the number of defectives is not less than or equal to acceptance number, then the answer is NO . Then , we reject the Lot.

So if we reject, we either do 100% inspection or return the lot to the supplier.

In a double sampling plan , the decision on acceptance/rejection  of the Lot is based on two samples.

The following symbol representation can be written as follows:

a. n1    →  number of size of sample 1

b. n2    → number of size of sample 2

c. c1    →  acceptance number for sample 1

d. c2    →  acceptance number for sample 2

e. d1    →  number of defectives in sample 1

f. d2   →  number of defectives in sample 2

Answer: trapezoid

Step-by-step explanation: A trapezoid is a quadrilateral

with exactly one pair of parallel sides.

Also, quadrilaterals are two-dimensional shapes.

So it's impossible that's its 3-d.

Answer:

A. trapezoid

Step-by-step explanation:

Step-by-step explanation:

18:27

=18/27

=2/3 or 2:3

Answer Choice 1

Take it step by step!

First find what sqrt(x-7) is like. Compare it to sqrt(x).

You can see that in sqrt(x), when x = 0, y = 0. However, in sqrt(x-7), when x = 7, y = 0. When y = 0, sqrt(x-7) is 7 more, which means it is shifted 7 units to the right.

Similarly, +8 means that whatever sqrt(x-7) is, you add 8 more to y. Adding on extra for y is just moving it up by 8 units.

Hope that helped,

-sirswagger21

Answer:

A) It fulfills the condition of binomial experiment

B) P (x=12) =0.1678

C)P ( x ≥16)= 0.1011

d) P (x>17) =0.0096 < 0.5

Step-by-step explanation:

A. The binomial probability distribution has the following four properties

1. the outcomes of each trial maybe classified into success and failure.

2) the probability of success p remains constant for all trials.

3) the successive trials are all independent.

4) the experiment is repeated a fixed number of times ,n.

These all conditions are fulfilled by the given question so it is a  binomial experiment.

B) P (x=12) = 20C12 (0.64)^12 * (1-0.64)^8= 0.1678

C) P ( x ≥16) = P (x=16) + P (x=17) + P (x=18) + P (x=19)+ P (x=20)

where

P (x=16)= 20C16 (0.64)^16 * (1-0.64)^4= 0.0645

P (x=17)= 20C17 (0.64)^17 * (1-0.64)^3= 0.0270

P (x=18)= 20C18 (0.64)^18 * (1-0.64)^2= 0.0080

P (x=19)=20C19 (0.64)^10 * (1-0.64)^1= 0.0015

P (x=20)= 20C20 (0.64)^20 * (1-0.64)^0= 0.0001

so

P ( x ≥16)= 0.0645+ 0.0270 +0.0080+ 0.0015+0.0001= 0.1011

d) P (x>17)= P (x=17) + P (x=18) + P (x=19)+ P (x=20)

                    =0.0270 +0.0080+ 0.0015+0.0001

                         =0.0096

From this we see that the probability of  more than 17  people who flush public toilets with their foot is unusual because it is far away from the mean which is supposed to be somewhere 0.5 in a given distribution.

Answer:

You have 1/60 of the original hair color left

Step-by-step explanation:

Add up the fractions

1/3 + 1/4 + 2/5

Get a common denominator of 60

1/3 * 20/20    + 1/4 * 15/15    + 2/5 * 12/12

20/60 + 15/60 + 24/60

59/60

The total is 1 or 60/60

60/60 - 59/60

1/60

You have 1/60 of the original hair color left

Answer:

the rate of change of the water depth when the water depth is 10 ft is;  [tex]\mathbf{\dfrac{dh}{dt} = \dfrac{-25}{100 \pi} \ \ ft/s}[/tex]

Step-by-step explanation:

Given that:

the inverted conical water tank with a height of 20 ft and a radius of 8 ft  is drained through a hole in the vertex (bottom) at a rate of 4 ft^3/sec.

We are meant to find the  rate of change of the water depth when the water depth is 10 ft.

The diagrammatic expression below clearly interprets the question.

From the image below, assuming h = the depth of the tank at  a time t and r = radius of the cone shaped at a time t

Then the similar triangles  ΔOCD and ΔOAB is as follows:

[tex]\dfrac{h}{r}= \dfrac{20}{8}[/tex]    ( similar triangle property)

[tex]\dfrac{h}{r}= \dfrac{5}{2}[/tex]

[tex]\dfrac{h}{r}= 2.5[/tex]

h = 2.5r

[tex]r = \dfrac{h}{2.5}[/tex]

The volume of the water in the tank is represented by the equation:

[tex]V = \dfrac{1}{3} \pi r^2 h[/tex]

[tex]V = \dfrac{1}{3} \pi (\dfrac{h^2}{6.25}) h[/tex]

[tex]V = \dfrac{1}{18.75} \pi \ h^3[/tex]

The rate of change of the water depth  is :

[tex]\dfrac{dv}{dt}= \dfrac{\pi r^2}{6.25}\ \dfrac{dh}{dt}[/tex]

Since the water is drained  through a hole in the vertex (bottom) at a rate of 4 ft^3/sec

Then,

[tex]\dfrac{dv}{dt}= - 4 \ ft^3/sec[/tex]

Therefore,

[tex]-4 = \dfrac{\pi r^2}{6.25}\ \dfrac{dh}{dt}[/tex]

the rate of change of the water at depth h = 10 ft is:

[tex]-4 = \dfrac{ 100 \ \pi }{6.25}\ \dfrac{dh}{dt}[/tex]

[tex]100 \pi \dfrac{dh}{dt} = -4 \times 6.25[/tex]

[tex]100 \pi \dfrac{dh}{dt} = -25[/tex]

[tex]\dfrac{dh}{dt} = \dfrac{-25}{100 \pi}[/tex]

Thus, the rate of change of the water depth when the water depth is 10 ft is;  [tex]\mathtt{\dfrac{dh}{dt} = \dfrac{-25}{100 \pi} \ \ ft/s}[/tex]

Answer:

the rate of change of the water depth when the water depth is 10 ft is;  

Step-by-step explanation:

Given that:

the inverted conical water tank with a height of 20 ft and a radius of 8 ft  is drained through a hole in the vertex (bottom) at a rate of 4 ft^3/sec.

We are meant to find the  rate of change of the water depth when the water depth is 10 ft.

The diagrammatic expression below clearly interprets the question.

From the image below, assuming h = the depth of the tank at  a time t and r = radius of the cone shaped at a time t

Then the similar triangles  ΔOCD and ΔOAB is as follows:

   ( similar triangle property)

h = 2.5r

The volume of the water in the tank is represented by the equation:

The rate of change of the water depth  is :

Since the water is drained  through a hole in the vertex (bottom) at a rate of 4 ft^3/sec

Then,

Therefore,

the rate of change of the water at depth h = 10 ft is:

Thus, the rate of change of the water depth when the water depth is 10 ft is;  

Step-by-step explanation:

Answer:

The Commutative property is represented by 5 + (-8) = -8 + 5.

Step-by-step explanation:

We are the following the following expression below;

5 + (-8) = -8 + 5

This property says that is any number is added to 0, then the result is the number itself, i.e.;

2 + 0 = 2 or (-7) + 0 = -7.

Suppose there are three numbers; a, b and c.

So, this property hold the condition that; a + (b + c) = (a + b) + c

If we add the second and third numbers and then add the first number to it or if we add the first and second numbers and then add the third number to it, the result will be the same.

Suppose there are two numbers 6 and 8.

This property states that if we add 6 + 8 or 8 + 6, both are equal, i,e;

6 + 8 = 8 + 6

14 = 14.

This property states the following condition;

a [tex]\times[/tex] (b + c) = (a [tex]\times[/tex] b) + (a [tex]\times[/tex] c)

So, 5 + (-8) = -8 + 5 is represented by the commutative property.