which substitution should be used to rewrite 16(x^3+1)^2-22(x^3+1)-3=0 as a equation?

Answer:

a = 30

b = 6/7

Step-by-step explanation:

The number of yeast cells after t hours is modeled by the following equation:

[tex]f(t) = a(1 + be^{-0.7t})[/tex]

In which a is the initial number of cells.

At time t = 0 the population is 30 cells

This means that [tex]a = 30[/tex]

So

[tex]f(t) = 30(1 + be^{-0.7t})[/tex]

And increasing at a rate of 18 cells/hour.

This means that f'(0) = 18.

We use this to find b.

[tex]f(t) = 30(1 + be^{-0.7t})[/tex]

So

[tex]f(t) = 30 + 30be^{-0.7t}[/tex]

Then, it's derivative is:

[tex]f'(t) = -30*0.7be^{-0.7t}[/tex]

We have that:

f'(0) = 18

So

[tex]f'(0) = -30*0.7be^{-0.7*0} = -21b[/tex]

Then

[tex]-21b = 18[/tex]

[tex]21b = -18[/tex]

[tex]b = -\frac{18}{21}[/tex]

[tex]b = \frac{6}{7}[/tex]

Answer:

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

And if we use the probability mass function we got:

[tex]P(X=0)=(4C0)(0.6)^0 (1-0.6)^{4-0}=0.0256[/tex]  

[tex]P(X=1)=(4C1)(0.6)^1 (1-0.6)^{4-1}=0.1536[/tex]  

And replacing we got:

[tex] P(X>1) =1- [0.0256 +0.1536]= 0.8208[/tex]

Step-by-step explanation:

Let X the random variable of interest, on this case we now that:  

[tex]X \sim Binom(n=4, p=0.6)[/tex]  

The probability mass function for the Binomial distribution is given as:  

[tex]P(X)=(nCx)(p)^x (1-p)^{n-x}[/tex]  

Where (nCx) means combinatory and it's given by this formula:  

[tex]nCx=\frac{n!}{(n-x)! x!}[/tex]  

We want to find the following probability:

[tex] P(X >1)[/tex]

And for this case we can use the complement rule and we got:

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

And if we use the probability mass function we got:

[tex]P(X=0)=(4C0)(0.6)^0 (1-0.6)^{4-0}=0.0256[/tex]  

[tex]P(X=1)=(4C1)(0.6)^1 (1-0.6)^{4-1}=0.1536[/tex]  

And replacing we got:

[tex] P(X>1) =1- [0.0256 +0.1536]= 0.8208[/tex]

Answer: The mean difference is between 799586.3 and 803257.9.

Step-by-step explanation: To estimate the mean difference for confidence interval:

Find the statistic sample:

For the traffic count, mean = 1835.8 and s = 1382607.3

The confidence interval is 90%, so:

α = [tex]\frac{1-0.9}{2}[/tex]

α = 0.05

The degrees of dreedom are:

df = n - 1

df = 10 - 1

df = 9

Using a t-ditribution table, the t-score for α = 0.05 and df = 9 is: t = 1.833.

Error will be:

E = [tex]t.\frac{s}{\sqrt{n} }[/tex]

E = 1.833.([tex]\frac{1382607.3}{\sqrt{10} }[/tex])

E = 801422.1

The interval is: mean - E < μ < E + mean

1835.8 - 801422.1 < μ < 1835.8+801422.1

-799586.3 < μ < 803257.9

The estimate mean difference in trafic count between 6th and 13th using 90% level of confidence is between 799586.3 and 803257.9.

Answer:

b. Skewed-left

Step-by-step explanation:

The histogram will be expressed with the x-axis representing the salaries, in growing amount to the right. The y-axis will represent the relative or absolute frequency.

We know that most of the players earn the minimum league wage. Then, we will have a high frequency in the low salaries classes, at the left of the histogram. A few players earn very high salaries, so we will have a right tail with high values for the salaries a little frequency.

There is no symmetry in this histogram and it is not uniform, as there is no representative mean salary.

As most of the data will be close to the left side, we can conclude that the histogram will be skewed-left.

The Histogram of salary data, with most having less salary is RIGHT Skewed

Given : Data of players' salary is concentrated towards towards most players having less ( minimum ) salary.

Right Skewness denotes a distribution where Tail is on the right side. This implies data is highly concentrated toward left side, ie lower independent variable (x - here 'salary') values.

Left Skewness denotes a distribution where Tail is on the left side. This implies data is highly concentrated towards right side, ie higher independent variable (x - here 'salary') values.

In this case : As more players have lower values of independent variable ie salary, so the data will be concentrated at left - having tail at right.

Hence, it will be Skewed Right

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Answer:

908360.67 lb-ft

Step-by-step explanation:

height of tank= 6 ft

diameter of the tank = 4 ft

density of water p = 62.4 lbs/ft

A is the cross sectional area of the tank

A = [tex]\pi r^{2}[/tex]

where r = diameter/2 =  4/2 = 2 ft

A = 3.142 x [tex]2^{2}[/tex] = 12.568 ft^2

work done = force x distance through which force is moved

work = F x d

Force  due to the water = pgAh

where g = acceleration due to gravity = 32.174 ft/s^2

Force  = 62.4 x 32.174 x 12.568 x 6 =  151393.44 lb

work done = force x distance moved

work = 151393.44 x 6 = 908360.67 lb-ft

Answer:

(a)650 ways

(b)650 ways

(c)676 ways

Step-by-step explanation:

There are 26 red and 26 black cards.

If a card is dealt to each of 2 players, we want to find out how many different ways this can be done.

(a)Both cards are red

If both cards are red:

The first red card can be dealt in 26 ways.

The second red card can be dealt in 25 ways.

Therefore: Both Red cards can be dealt in: 26 X 25 = 650 ways

(b)Both cards are black

If both cards are black:

The first black card can be dealt in 26 ways.

The second black card can be dealt in 25 ways.

Therefore: Both black cards can be dealt in: 26 X 25 = 650 ways

(c)One card is black and the other is red.

The red card can be dealt in 26 ways.

The black card can be dealt in 26 ways.

Therefore: Both cards can be dealt in: 26 X 26 = 676 ways

Step-by-step explanation:

a) 2x = 8 x 3

2x = 24

x = 12

b) 3x = 12

x = 4

Answer:

the answer is 157

Step-by-step explanation:

7 +10= 17

17+20=37

37+40=77

77+80=157

157+160=317

At the beginning you add +10. Every sequence, you need to multiply that number x2. For example: 10 x 2=20...

Answer:

g(x) is greater

Step-by-step explanation:

Answer:

Step-by-step explanation: [tex]\frac{5}{3}[/tex]÷[tex]\frac{1}{3}[/tex] =

(Decimal: 0.555556)

Answer:

[tex]\sum_{i=1}^n w_i *X_i = 2.8*24 = 67.2[/tex]

And for this case we want a gpa of 3.0 taking in count that in this semester he/ she is going to take 16 credits so then the new mean would be given by:

[tex] \bar X_f = \frac{\sum_{i=1}^n w_i *X_i+w_f *X_f }{24+16} = 3.0[/tex]

And we can solve for [tex]\sum_{i=1}^n w_f *X_f [/tex] and solving we got:

[tex] 3.0 *(24+16) =\sum_{i=1}^n w_i *X_i +\sum_{i=1}^n w_f *X_f [/tex]

And from the previous result we got:

[tex] 3.0 *(24+16) =67.2 +\sum_{i=1}^n w_f *X_f[/tex]

And solving we got:

[tex] \sum_{i=1}^n w_f *X_f =120 -67.2= 52.8[/tex]

And then we can find the mean with this formula:

[tex] \bar X_2 = \frac{\sum_{i=1}^n w_f *X_f}{16}= \frac{52.8}{16}=16=3.3[/tex]

So then we need a 3.3 on this semester in order to get a cumulate gpa of 3.0

Step-by-step explanation:

For this case we know that the currently mean is 2.8 and is given by:

[tex] \bar X = \frac{\sum_{i=1}^n w_i *X_i }{24} = 2.8[/tex]

Where [tex] w_i[/tex] represent the number of credits and [tex]X_i[/tex] the grade for each subject. From this case we can find the following sum:

[tex]\sum_{i=1}^n w_i *X_i = 2.8*24 = 67.2[/tex]

And for this case we want a gpa of 3.0 taking in count that in this semester he/ she is going to take 16 credits so then the new mean would be given by:

[tex] \bar X_f = \frac{\sum_{i=1}^n w_i *X_i+w_f *X_f }{24+16} = 3.0[/tex]

And we can solve for [tex]\sum_{i=1}^n w_f *X_f [/tex] and solving we got:

[tex] 3.0 *(24+16) =\sum_{i=1}^n w_i *X_i +\sum_{i=1}^n w_f *X_f [/tex]

And from the previous result we got:

[tex] 3.0 *(24+16) =67.2 +\sum_{i=1}^n w_f *X_f[/tex]

And solving we got:

[tex] \sum_{i=1}^n w_f *X_f =120 -67.2= 52.8[/tex]

And then we can find the mean with this formula:

[tex] \bar X_2 = \frac{\sum_{i=1}^n w_f *X_f}{16}= \frac{52.8}{16}=16=3.3[/tex]

So then we need a 3.3 on this semester in order to get a cumulate gpa of 3.0

Answer:

csc 270° is the answer.

Answer: time = 20 seconds

Step-by-step explanation:

h(t) = -16t² + 316t + 80

The shape of this graph is an upside parabola ∩.  

It lands on the ground when height (h) = 0

Set the equation equal to zero, factor, and solve for t.

0 =  -16t² + 316t + 80

0 =  4t² - 79t - 20              divided both sides by -4

0 = (4t + 1)(t - 20)               factored the equation

t = -1/4      t = 20              Applied Zero Product Property and solved for t

Since we know time cannot be negative, disregard t = -1/4

The only valid solution is: t = 20

Answer:

543

Step-by-step explanation:

let x= total salary

0.25x=135.75

x=543

Answer:

[tex]\$ \: 543.00[/tex]

Step-by-step explanation:

[tex]25\% \times x =135.75[/tex]

[tex]1/4 \times x =135.75[/tex]

[tex]0.25 \times x =135.75[/tex]

[tex]x=135.75 \times 4[/tex]

[tex]x=543[/tex]

Answer:

1  3/10

Step-by-step explanation:

9/8  +7/40

Get a common denominator of 40

9/8 *5/5 + 7/40

45/40 + 7/40

52/40

Rewriting as

40/40 +12/40

1 + 3/10

1  3/10

Answer:

1 3/10

Step-by-step explanation:

First, you need to get a common denominator:

8x5=40 <-- common denominator

45/40+7/40= 52/40

yes you can simplify it.

your final answer will be: 1 3/10

Answer:

None

Step-by-step explanation:

The answers are:

1. g(10) -31

2. x= -17/3

3. f(3)= 2

4.x= √30

5. h(-2)= 1

6. x= 0

7. h(a)= 1

In mathematics, a function is represented as a rule that produces a distinct result for each input x. In mathematics, a function is indicated by a mapping or transformation. Typically, these functions are identified by letters like f, g, and h. The collection of all the values that the function may input while it is defined is known as the domain. The entire set of values that the function's output can produce is referred to as the range. The set of values that could be a function's outputs is known as the co-domain.

Given:

f(x) = x² – 7

g(x) = -3x - 1

j(x)= 2x-9

h(x) = 1

1. g(10)= -3(10) -1 = -30 - 1= -31

2. g(x) = 16

-3x- 1= 16

-3x = 17

x= -17/3

3. f(3)= (3)² – 7 = 9- 7= 2

4. f(x)= 23

x² – 7=  23

x² = 30

x= √30

5. h(-2)= 1

6. x= 0

7. h(a)= 1

8. S(-1) = 3

The value of function s(a) at a=-1 is 3.

10. g(4) = -1

The value of function g(a) at a=4 is -1.

11. h(2) = 8

The value of function h(a) at a=2 is 8.

12. k(2) = 9​

The value of function k(a) at a= 2 is 9.

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Answer:

A linear equation is an equation with two variables whose graph is a line. The graph of the linear equation is a set of points in the coordinate plane that all are solutions to the equation. If all variables represent real numbers one can graph the equation by plotting enough points to recognize a pattern and then connect the points to include all points.If you want to graph a linear equation you have to have at least two points, but it's usually a good idea to use more than two points. When choosing your points try to include both positive and negative values as well as zero

Step-by-step explanation:

Answer:

The answer would be C because the y-intercept is when x is equal to 0

please mark me brainliest

Answer:

[tex]\frac{1}{12}[/tex]

Step-by-step explanation:

The number with the smallest denominator is the larger number and [tex]\frac{1}{12}[/tex] is the number with the smallest denominator out of [tex]\frac{1}{12} , \frac{1}{32} , \frac{1}{48} , \frac{1}{18}[/tex].

Answer:

1/12

Step-by-step explanation:

Start with a number, for example 100.

Now divide 100 by several numbers which are greater and greater:

100/1 = 100

100/2 = 50

100/4 = 25

100/10 = 10

100/100 = 1

As you divide the same number, 100, by a greater number, the result becomes smaller.

As we divide 100 by 1, then by 2, then by 4, etc., we are always dividing 100 by a greater and greater number. The result is smaller and smaller, 100, 50, 25, etc. If you always divide the same number by other numbers, the larger the number you divide by, the smaller the result.

Numbers in order from greatest to smallest:

1/12, 1/18, 1/32, 1/48

Answer: The greatest number is 1/12

Answer:

y = -3x + 3

[tex]y=\frac{1}{3}x-7[/tex]

Step-by-step explanation:

Slope of a line passing through two points ([tex]x_1, y_1[/tex]) and [tex](x_2, y_2)[/tex] is determined by the formula,

Slope = [tex]\frac{(y_2-y_1)}{(x_2-x_1)}[/tex]

If these points are (0, 3) and (3, -6),

Slope of the line passing through these lines = [tex]\frac{3+6}{0-3}[/tex] = (-3)

Equation of the line which passes through (0, 3) and slope = (-3),

y - y' = m(x - x')

y - 3 = (-3)(x- 0)

y - 3 = -3x

y = -3x + 3

Now slope of another line that passes through (3, -6) and (0, -7),

m' = [tex]\frac{(-6+7)}{(3-0)}[/tex]

m' = [tex]\frac{1}{3}[/tex]

Equation of the line that passes through (0, -7) and slope = [tex]\frac{1}{3}[/tex]

y - (-7) = [tex]\frac{1}{3}(x-0)[/tex]

y + 7 = [tex]\frac{1}{3}x[/tex]

y = [tex]\frac{1}{3}x-7[/tex]

Therefore, system of linear equations are,

y = -3x + 3

[tex]y=\frac{1}{3}x-7[/tex]

Answer:

The mode would not change

Step-by-step explanation:

Mode is the frequency of 1 number. In this case, the mode is 3. If we add 8, the frequency of 3 would not change; there would still be 4 3's, and 3 would still have the most of itself.

Answer:

The 1st graph

Step-by-step explanation:

The quickest and easiest way is to just graph y < x² + 4x + 5. When you do so you should be able to see your answer.

Answer:

12.5% probability that when a couple has three​ children, there are exactly 0 girls.

Step-by-step explanation:

A probability is the number of desired outcomes divided by the number of total outcomes.

Possible outcomes:

b for boy, g for girl

g - g - g

g - g - b

g - b - g

g - b - b

b - g - g

b - g - b

b - b - g

b - b - b

8 outcomes, one of which (b - b - b) with exactly 0 girls.

So

1/8 = 0.125

12.5% probability that when a couple has three​ children, there are exactly 0 girls.

The probability that when a couple has three​ children, there are exactly 0 girls is 12.5%

Here we assume b for boy, g for girl

Now the probability conditions are

g - g - g

g - g - b

g - b - g

g - b - b

b - g - g

b - g - b

b - b - g

b - b - b

There are 8 outcomes, one of which (b - b - b) with exactly 0 girls.

So

[tex]= 1\div 8[/tex]

= 0.125

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Answer:

[tex]\cos (\theta)[/tex]

Step-by-step explanation:

[tex]\dfrac{\tan (\theta) \cot (\theta)}{\sec (\theta)}= \\\\\\\dfrac{\dfrac{\sin (\theta)}{\cos (\theta)}\cdot \dfrac{\cos (\theta)}{\sin (\theta)}}{\dfrac{1}{\cos (\theta)}}= \\\\\\1\cdot \cos (\theta)=\\\\\\\boxed{\cos (\theta)}[/tex]

Hope this helps!

Answer:

The explanation is:

All interior angles in an equilateral triangle are congruent, making them all 60° by the sum of angles in a triangle. Because alternate interior angles of parallel lines are congruent, x = 60°.

Answer:

-2x² + 15

Step-by-step explanation:

Step 1: Add like terms

4x² - 6x² = -2x²

-10x + 10x = 0

12 + 3 = 15

Step 2: Rewrite

-2x² + 15

[tex](8 - 10x + 3) + ( - 12 + 10x + 12)[/tex]

[tex](11 - 10x) + (10x)[/tex]

[tex] 11 - 10x + 10x[/tex]

[tex] = 11[/tex]

Answer:

Haha proofs are an interesting thing. Usually, nothing is to scale, which is why you can't measure anything. They are pretty annoying, but it helps to know why certain things are the way that they are and develop justification skills for higher level math.

Sorry to discourage you, but you're going to see "Justify" quite a lot in calculus and beyond which is basically a more informal version of a proof

you can never escape it tbh lol

We can't just measure the two figures to see if they are congruent as congruence is about shape and size.

It should be noted that congruence simply means that the shapes have identical length, angles, and size.

Therefore, we can't just measure the two figures to see if they are congruent as congruence is about shape and size.

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Answer:

D.

Step-by-step explanation:

Deus ex machina is the plot device of using something very improbable to resolve a situation.

Answer:

It's D: No, there is not enough information given.

Step-by-step explanation:

just took the quiz

The correct answer option D which is No, there is not enough information given.

A parallelogram is a quadrilateral having four sides with two opposite sides parallel to each other. The sum of the angles suspended by all the four sides of the parallelogram is 360.

Using VX = WZ and m∠ZVX = m∠XWZ, we have a side and an angle. In order to prove the triangles congruent by SAS, we must have two sides and the angle between them. With the information we have now, we would have to have VZ = WX. However, we are not given that information.

We do have that ZX = ZX by the reflexive property, but this is not SAS, as the angle we have is not between the two sides.

Therefore correct answer option D which is No, there is not enough information given.

The complete figure is attached with the answer below.

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Answer:

-17.32

Step-by-step explanation:

(1319- 19*797)/798 = -17.3233

Answer:

The x intercepts are (7,0) and (-4,0)

Step-by-step explanation:

y = x^2 – 3x - 28

Set y=0

0 = x^2 – 3x - 28

Factor.  What 2 numbers multiply to -28 and add to -3

-7*4 = -28

-7+4 = -3

0 = (x-7)(x+4)

Using the zero product property

0 = (x-7)      0 = x+4

x=7              x = -4

The x intercepts are (7,0) and (-4,0)