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simplify the equation​

Answer:

18.333

Step-by-step explanation:

Answer:

C . The graph of the polynomial has zeros at (-7,0) and (2,0)

Step-by-step explanation:

f(x) = (x + 7)(x - 2)

Zero's obtained:

Coordinates:

Correct answer choice is:

C . The graph of the polynomial has zeros at (-7,0) and (2,0)

Answer:

Step-by-step explanation:

A general equation of a hyperbola is

 x^2     y^2

-------- - ------- = 1   (This applies only when the center of the hyperbola

 a^2     b^2                               is at (0, 0)  ).

You must compare the given equations to this standard form to identify which represents the hyperbola shown, and also you must share the illustration of the hyperbola.

The equation represents the hyperbola shown in the graph is  (y - 1)² / 9 - (x + 4)² / 4  = 1

A hyperbola is a type of smooth curve lying in a plane, defined by its geometric properties or by equations for which it is the solution set.

A hyperbola has two pieces, called connected components or branches, that are mirror images of each other and resemble two infinite bows.

Given that, a graph, showing hyperbola, we need to find the equation,

We have the general equation for up - down facing hyperbola as

(y - k)² / b²- (x - h)² / a²  = 1.

Let's start listing the properties of this graph -

Taking a look at the graph we see that the center point of our hyperbola here is (- 4, 1).

Therefore, (h, k) = (- 4,1).

This is the semi distance from the center to one of the vertices. Here it will be the distance from points (- 4,1) and (- 4,4) or 3 unit difference.

Therefore, a = 3.

That gives asymptotes. Now remember that it will be in the form

y = ± b / a.

We already know a = 3, so we have to find b.

Looking at this graph we can say that another point besides (- 4,1) that lies on the "dotted line" is (- 2, - 2).

Calculating the slope of the dotted line would be as follows,

Given: (- 4,1) and (- 2, - 2)

Slope = - 2 + 4 / - 2 - 1 = 2 / 3

We have the equation y = 2 / 3x.

Therefore, b = 2.

Let's substitute to equation...

h = - 4, k = 1, b = 2, a = 3

(y - 1)² / (3)²- (x + 4)² / (2)²  = 1

(y - 1)² / 9 - (x + 4)² / 4  = 1

Hence, the equation represents the hyperbola shown in the graph is  (y - 1)² / 9 - (x + 4)² / 4  = 1

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The complete question is attached

Answer:

2.33 units

Step-by-step explanation:

[tex]\tan 25\degree =\frac{AC}{5}\\\\0.46630 = \frac{AC}{5}\\\\AC = 0.46630 \times 5\\AC =2.3315\\AC = 2.33 \: units[/tex]

Step-by-step explanation:

tags is not a fixed cost

Answer:

The solutions to the system of equations are [tex]y=4,\:x=5[/tex].

Step-by-step explanation:

To solve the system [tex]\begin{bmatrix}4x+5y=40\\ 6x+3y=42\end{bmatrix}[/tex]

First,

[tex]\mathrm{Multiply\:}4x+5y=40\mathrm{\:by\:}3\:\mathrm{:}\:\quad \:12x+15y=120\\\\\mathrm{Multiply\:}6x+3y=42\mathrm{\:by\:}2\:\mathrm{:}\:\quad \:12x+6y=84[/tex]

[tex]\begin{bmatrix}12x+15y=120\\ 12x+6y=84\end{bmatrix}[/tex]

Subtract the first equation from the second equation

[tex]12x+6y=84\\\underline{-12x-15y=-120}\\-9y=-36[/tex]

Solve [tex]-9y=-36[/tex] for y:

[tex]\frac{-9y}{-9}=\frac{-36}{-9}\\y=4[/tex]

For [tex]12x+15y=12[/tex] plug in [tex]y=4[/tex] and solve for x

[tex]12x+15\cdot \:4=120\\12x=60\\x=5[/tex]

The solutions to the system of equations are:

[tex]y=4,\:x=5[/tex]

Answer:

4/15

Step-by-step explanation:

The total number of spins completed is 6+8+7+9 = 30

The letter B came up 8 times

P(B) = number of B's over total

P(B) = 8/30 = 4/15

Answer:

5 sessions each

Step-by-step explanation:

Let the personal training sessions be x.

Then at Silver Gym Sarah would spend:

And at Fit Factor she would spend:

Since total costs are same, the amounts will be equal:

So Sarah would buy 5 training sessions for each of the gyms.

And she would spend $185 at each.

Answer:

Let's denote:

x: number of ticket 28$

y: number of ticket 40$

Then, we have:

x + y =5000

28x + 40y = 153200

=> 28(5000 - y) + 40y = 153200

=> 12y = 153200 - 140000

=> 12y =13200

=> y = 1100 (ticket 40$)

=> x = 5000 - 1100 = 3900 (ticket 28$)

Answer:

The theoretical probability of drawing a red marble is 1/3.

Step-by-step explanation:

1. Add all of the marbles together to get total marbles. 16 + 12 + 8 = 36.

2. Create a fraction, with numerator being favorable outcomes and denominator being total possible outcomes. In this case it would be 12/36.

3. Since it is asking for a reduced fraction, simplify 12/36 to 1/3.

A fraction is the numerator divided by the denominator best describes a fraction.

Given,

- A fraction is the denominator divided by the numerator.

- A fraction is the numerator divided by the denominator.

- A fraction is the numerator multiplied by the denominator.

- A fraction is the denominator multiplied by the numerator.

We need to find which option best describes a fraction.

A fraction has two parts: Numerator and Denominator.

It is in the form of Numerator / Denominator.

We have,

- A fraction is the denominator divided by the numerator.

It is written as denominator / Numerator.

- A fraction is the numerator divided by the denominator.

It is written as Numerator / Denominator

- A fraction is the numerator multiplied by the denominator.

It is written as Numerator x Denominator.

- A fraction is the denominator multiplied by the numerator.

It can be written as Denominator x Numerator.

We see that the option "a fraction is a numerator divided by the denominator" is the correct answer.

Thus A fraction is the numerator divided by the denominator best describes a fraction.

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Answer:12 months

Step-by-step explanation:

400+400=800 so  950-800=150 1800/150=12

Answer:

mean: 46.63636

median: 34

mode: 87

range:95

How To:

Step 1 : To find Mean

    Average = ( 1 + 5 + 5 + 7 + 8 + 10 ) / 6

             =36 / 6

    Mean = 6

Step 2 : To find Median

   Middle value = ( 5 + 7 ) / 2

               = 12 / 2

    Median = 6

Step 3 : To find Mode

   Mode = 5 (The number with more repetition, here 5 is repeated two times)

Step 4 : To find Range

    Range = Largest number - Smallest number

       = 10-1

       = 9

Range = 9

Answer:

Mean: 46.6

Mode: 87

Median: 34

Range: 95

Step-by-step explanation:

Mean: (finding the average)

Median: (the middle number of the data set)

Mode: (the most number repeated from the data set)

Range: (is the difference between the highest value and the lowest value)

first arrange the following data set.

23, 87, 19, 34, 37, 87, 81, 5, 14, 100, 26

so:

5, 14, 19, 23, 26, 34, 37, 81, 87, 87, 100

Lets us first find the mean by adding up all the numbers and dividing it by the amount of numbers in the data set.

Mean: 5 + 14 + 19 + 23 + 26 + 34 + 37 + 81 + 87 + 87 + 100 = 513/11 = 46.6

Mode: 87

Median: 34

Range: 100 - 5 = 95

Answer:

228 of them are made from wool, but there is no enough information to determine how many would he has in stock.

Step-by-step explanation:

Mr Ollivander's stuffed bear shop has 456 bears in stock, and exactly half of them are made from wool, this means that 1/2 of 456 are made from wool

1/2 of 456 = 1/2 × 456 = 456/2 = 228.

That is 228 of them are made from wool.

However, nothing tells us that this is all he has in his stock. There is no information available to determine how many would he has in stock.

Answer:

1320 feet

Step-by-step explanation:

All we have to do is multiply the rate of change of altitude by the time it took the altitude to change.

The altitude of an airplane is decreasing at a rate of 44 feet per second. After 30 seconds, the change is altitude is:

44 * 30 = 1320 feet

The altitude of the airplane has changed by 1320 feet.

Answer:

P-value (t=2.58) = 0.0066.

Note: as we are using the sample standard deviation, a t-statistic is appropiate instead os a z-statistic.

As the P-value (0.0066) is smaller than the significance level (0.05), the effect is  significant.

The null hypothesis is rejected.

There is enough evidence to support the claim that the population mean μ exceeds 2.4.

Step-by-step explanation:

This is a hypothesis test for the population mean.

The claim is that the population mean μ exceeds 2.4.

Then, the null and alternative hypothesis are:

[tex]H_0: \mu=2.4\\\\H_a:\mu> 2.4[/tex]

The significance level is 0.05.

The sample has a size n=45.

The sample mean is M=2.5.

As the standard deviation of the population is not known, we estimate it with the sample standard deviation, that has a value of s=0.26.

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

[tex]s_M=\dfrac{s}{\sqrt{n}}=\dfrac{0.26}{\sqrt{45}}=0.0388[/tex]

Then, we can calculate the t-statistic as:

[tex]t=\dfrac{M-\mu}{s/\sqrt{n}}=\dfrac{2.5-2.4}{0.0388}=\dfrac{0.1}{0.0388}=2.58[/tex]

The degrees of freedom for this sample size are:

[tex]df=n-1=45-1=44[/tex]

This test is a right-tailed test, with 44 degrees of freedom and t=2.58, so the P-value for this test is calculated as (using a t-table):

[tex]P-value=P(t>2.5801)=0.0066[/tex]

As the P-value (0.0066) is smaller than the significance level (0.05), the effect is  significant.

The null hypothesis is rejected.

There is enough evidence to support the claim that the population mean μ exceeds 2.4.

Answer:

(a) Probability that 2 or fewer will withdraw is 0.2061.

(b) Probability that exactly 4 will withdraw is 0.2182.

(c) Probability that more than 3 will withdraw is 0.5886.

(d) The expected number of withdrawals is 4.

Step-by-step explanation:

We are given that a university found that 20% of its students withdraw without completing the introductory statistics course.

Assume that 20 students registered for the course.

The above situation can be represented through binomial distribution;

[tex]P(X =r) = \binom{n}{r} \times p^{r} \times (1-p)^{n-r};x=0,1,2,3,......[/tex]

where, n = number of trials (samples) taken = 20 students

            r = number of success  

            p = probability of success which in our question is probability  

                  that students withdraw without completing the introductory  

                  statistics course, i.e; p = 20%

Let X = Number of students withdraw without completing the introductory statistics course

So, X ~ Binom(n = 20 , p = 0.20)

(a) Probability that 2 or fewer will withdraw is given by = P(X [tex]\leq[/tex] 2)

P(X [tex]\leq[/tex] 2) =  P(X = 0) + P(X = 1) + P(X = 2)

=  [tex]\binom{20}{0} \times 0.20^{0} \times (1-0.20)^{20-0}+ \binom{20}{1} \times 0.20^{1} \times (1-0.20)^{20-1}+ \binom{20}{2} \times 0.20^{2} \times (1-0.20)^{20-2}[/tex]

=  [tex]1 \times1 \times 0.80^{20}+ 20 \times 0.20^{1} \times 0.80^{19}+ 190\times 0.20^{2} \times 0.80^{18}[/tex]

=  0.2061

(b) Probability that exactly 4 will withdraw is given by = P(X = 4)

                      P(X = 4) =  [tex]\binom{20}{4} \times 0.20^{4} \times (1-0.20)^{20-4}[/tex]

                                 =  [tex]4845\times 0.20^{4} \times 0.80^{16}[/tex]

                                 =  0.2182

(c) Probability that more than 3 will withdraw is given by = P(X > 3)

P(X > 3) =  1 - P(X [tex]\leq[/tex] 3) = 1 - P(X = 0) - P(X = 1) - P(X = 2) - P(X = 3)

=  [tex]1-(\binom{20}{0} \times 0.20^{0} \times (1-0.20)^{20-0}+ \binom{20}{1} \times 0.20^{1} \times (1-0.20)^{20-1}+ \binom{20}{2} \times 0.20^{2} \times (1-0.20)^{20-2}+\binom{20}{3} \times 0.20^{3} \times (1-0.20)^{20-3})[/tex]

=  [tex]1-(1 \times1 \times 0.80^{20}+ 20 \times 0.20^{1} \times 0.80^{19}+ 190\times 0.20^{2} \times 0.80^{18}+1140\times 0.20^{3} \times 0.80^{17})[/tex]

=  1 - 0.4114 = 0.5886

(d) The expected number of withdrawals is given by;

                        E(X)  =  [tex]n\times p[/tex]

                                 =  [tex]20 \times 0.20[/tex] = 4 withdrawals

Answer:

I also belive for Part A the second one is the answer because it equals 120 Part B is 120 pints! Good Luck! And I hope this Helps!

Answer:

B

Step-by-step explanation:

Answer:

4/15

Step-by-step explanation:

Bag A

3 red marbles and 6 blue marbles.  = 9 marbles

P(blue) = blue/total =6/9 = 2/3

Bag B

6 green marbles and 4 yellow marbles.  = 10 marbles

P(yellow) = yellow/total=4/10 = 2/5

P(blue,yellow) = 2/3 * 2/5 = 4/15

Answer:

3x + 2y = -2

Step-by-step explanation:

Given Equation is − 2 x  +  3 y  =  12

3 y  = 2 x  +  12

y =  ( 2 /3 )  y  +  12

Slope of this line is  m  =  2/ 3

Slope of Line A m a  =  2

Slope of Line B  m b  =  2/ 3

Slope of Line C  m c  =  − ( 2 /3 )

Slope of Line D  m d  =  −  ( 3 /2 )

since  m d  =  − 1 /m  ,  D  is perpendicular to the given line

Answer:

D

Step-by-step explanation:

I'm really sry if it's wrong!

Answer:

[tex]45\pi$ square inches[/tex]

Step-by-step explanation:

The radius, r of the expanding circle of oil is modeled by the function:

[tex]r=3\sqrt{s}[/tex] , where s is time in seconds.

When s=5

Radius [tex]r(5)=3\sqrt{5}$ inches[/tex]

Area of a circle [tex]=\pi r^2[/tex]

Therefore, the area of the oil spill when s=5 seconds

[tex]=\pi* (3\sqrt{5})^2\\=45\pi$ square inches[/tex]

The area of the spill when s=5 seconds is 45pi square inches.

Answer:

The answer is 0.31

Step-by-step explanation:

Old Method                                       New Method                          .

Mean                      73.5625                  Mean            75.70588

Standard Error        3.143736             Standard Error  2.923994

Median                    72                          Median            75

Mode                       90                          Mode               64

Standard deviation  12.57494           Standard deviation 12.05594

Sample Variance     158.1292            Sample Variance     145.3456

Kurtosis                     -1.14544              Kurtosis                   -0.76646

Skewness                 0.171025             Skewness                0.091008

Range                       39                        Range                      41

Minimum                   55                        Minimum                 56

Maximum                  94                        Maximum                 97

Sum                          1177                        Sum                        1287

Count                         16                         Count                      17

State the hypotheses. The first step is to state the null hypothesis and an alternative hypothesis.

Null hypothesis: μNew< μOld

Alternative hypothesis: μNew > μOld

Note that these hypotheses constitute a one-tailed test. The null hypothesis will be rejected if the mean difference between sample means is too small.

Formulate an analysis plan. For this analysis, the significance level is 0.05. Using sample data, we will conduct a two-sample t-test of the null hypothesis.

Analyze sample data. Using sample data, we compute the standard error (SE), degrees of freedom (DF), and the t statistic test statistic (t).

[tex]SE=\sqrt{\frac{S_1^2}{n_1} +\frac{S_2^2}{n_2} } \\\\SE=4.29[/tex]

DF = 31

[tex]t = \frac{(x_1-x_2)-d}{SE} \\\\t = - 0.4997[/tex]

where s1 is the standard deviation of sample 1, s2 is the standard deviation of sample 2, n1 is the size of sample 1, n2 is the size of sample 2, x1 is the mean of sample 1, x2 is the mean of sample 2, d is the hypothesized difference between population means, and SE is the standard error.

The observed difference in sample means produced a t statistic of - 0.499. We use the t Distribution Calculator to find P(t < - 0.499) = 0.311

Therefore, the P-value in this analysis is 0.311.

Interpret results. Since the P-value (0.311) is greater than the significance level (0.05), we cannot reject the null hypothesis.

From the above test we do have sufficient evidence in the favor of the claim that new method is efficient than the old method.

Answer:3

Step-by-step explanation:

edg

Answer:

Option B (4,5)

Step-by-step explanation:

The integers (4, 5) do not have real zero.

Knowing what zeros represent can assist us in determining when and how to locate the zeros of functions given their expressions and a function's graph. The value of x when the function itself reaches zero is typically referred to as a function's zero.

A function's zero can take many different forms, but as long as they have a y-value of zero, we will consider them to be the function's zero.

Given Expression

f(x) = x³ + 9x² + 8x - 5

to find which is not a real zero,

condition of real zero is for any function f(a , b) if f(a).f(b) < 0 the function have at least a zero.

1: (-8, -7)

f(-8).f(-7) = [(-8)³ + 9(-8)² + 8(-8) - 5][(-7³)  + 9(-7)² + 8(-7) - 5]

f(-8).f(-7) = (-5)(37)

f(-8).f(-7) = -185 < 0 points  have at least a zero

2:  (4, 5)

f(4).f(5) = [(4)³ + 9(4)² + 8(4) - 5][(5³)  + 9(5)² + 8(5) - 5]

f(4).f(5) = 235 x 385

f(4).f(5) = 94,475 > 0

points do not have any zeros

3: (0, 1)

f(0).f(1) = [(0)³ + 9(0)² + 8(0) - 5][(1³)  + 9(1)² + 8(1) - 5]

f(0).f(1) = -5 x 13

f(0).f(1) = -65 < 0

points  have a zero

4: (–2, –1)

f(-2).f(-1) = [(-2)³ + 9(-2)² + 8(-2) - 5][(-1³)  + 9(-1)² + 8(-1) - 5]

f(-2).f(-1) = 7 x (-5)

f(-2).f(-1) = -35 < 0

points  have a zero

Hence only point  (4, 5) do not have a zero.

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Answer:

D

Step-by-step explanation:

since sam invest the least, let a be the amount invested by sam

sam = a

paul = a + 5000

bob = a + 5000 + 4000

3a + 14000 = 50000

3a = 36000

a = 12000

thus sam is 12000, paul is 17000 and Bob is 21000

therefore the ratio of B:P:S is 21:17:12

profit by paula is 17/50 x 70000 = 23800

The profit by Paula is 17/50 x 70000 = 23800.

We have given that Bob, Paula and Sam invest $50000 in a business. Bob invests $4000 more than Paul does and Paul invests $5000 more than Sam does. If the total profit was $70000

Since sam invest the least, let a be the amount invested by sam

Therefore we get,

sam = a

The investment of Paul = a + 5000

Bob = a + 5000 + 4000

3a + 14000 = 50000

3a = 36000

divide both sides by 3 so we get,

a=36000/3

a = 12000

Therefore, sam is 12000,

paul =5000+12000=17000 and

Bob =12000+9000= 21000

Therefore the ratio of B:P:S is 21:17:12

The profit by Paula is 17/50 x 70000 = 23800.

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Answer:69°43'

Step-by-step explanation:

Complementary angles add up to 90

Let them complement be y

y+20°17`=90°

Collect like terms

y=90-20°17' 20°17'=1217/60

y=90-1217/60

y=(60x90 -1 x 1217)/60

y=(5400-1217)/60

y=4183/60

y=69°43'

Answer:

4.24

Step-by-step explanation:

To solve this, use the Pythagorean therom. A^2 + b^2 = C^2

in this case a = 3  and b = 3

so 9 + 9 =  sqrt 18  

4.24

Answer:3√(2)

Step-by-step explanation:

DF=3

EF=3

DE=√(3^2 + 3^2)

DE=√(3x3 + 3x3)

DE=√(9+9)

DE=√(18)

DE=√(2 x 9)

DE=√(2) x √(9)

DE=√(2) x 3

DE=3√(2)

Answer:

Black Line     y = 3 + 2x ,     y = 2x +3

Red Line       y = -2 - .5x.     y = -.5x -2

vice versa

Step-by-step explanation:

For the black line, the lines intersects y at coordinate (0,3) and that would be b. To find the slope, use the equation rise / run. It rises 4 and runs 2. Putting this into an equation 4/2, it would be 2 as the constant. In other words, it would be 2x. Therefore, the function for the black line is y = 3 + 2x

For the red line, using the same explanation from the black line, the line intersects y at -2, and the slope would be -.5x, since it runs downwards 2 and runs 4, and since it runs downwards, a negative sign would be necessary in front of the slope.