Which equation represents y = x^2 + 16x + 70 in vertex form?


y = (x + 8)^2 − 16


y = (x + 8)^2 − 64


y = (x + 8)^2 + 68


y = (x + 8)^2 + 6

One marker would cost approx. $0.03

The law of large numbers in probability, is a theorem that describes the result of performing the same experiment a large number of times because the average of the results obtained from a large number of trials is close enough to the expected value.

So, according to this definition and the situation given , the correct answer is option B - if 800 people are randomly surveyed about the TV shows they watch, about 400 of them will be women; because there are larger number of experiment.

Part B:

To get the expected value of a t-shirt we will multiply each of the 3 prices by the associated probability, and then add up these three products-

[tex](24\times\frac{1}{6})+(30\times\frac{1}{2})+(36\times\frac{1}{3})[/tex]

=4 + 15 + 12 = $31

Hence, option C is correct.

Answer:

1.  If 800 people are randomly surveyed about the TV shows they watch, about 400 of them will be women.

2. $31

Step-by-step explanation:

Got it right on the test.

[tex]6r+5=11r\ \ \ \ |\text{subtract 6r from both sides}\\\\5=5r\ \ \ \ |\text{divide both sides by 5}\\\\\boxed{r=1}\\-------------------------\\\dfrac{2x-4}{2}=6x+3\\\\\dfrac{2x}{2}-\dfrac{4}{2}=6x+3\\\\x-2=6x+3\ \ \ \ \ |\text{add 2 to both sides}\\\\x=6x+5\ \ \ \ |\text{subtract 6x from both sides}\\\\-5x=5\ \ \ \ \ |\text{divide both sides by -5}\\\\\boxed{x=-1}[/tex]

4x³ - 20x² + 24x = 0

4x(x² - 5x + 6) = 0

4x(x - 2)(x - 3) = 0

4x = 0        x - 2 = 0          x - 3 = 0

 x = 0            x = 2              x = 3

Answer: 0, 2, 3  

Factoring and solving a quadratic equation, it is found that the roots of the equation are:

[tex]x = 0[/tex]

[tex]x = 2[/tex]

[tex]x = 3[/tex]

The equation given is:

[tex]4x^3 - 20x + 24x = 0[/tex]

Factoring the common term:

[tex]4x(x^2 - 5x + 6) = 0[/tex]

For the roots:

[tex]4x = 0 \rightarrow x = 0[/tex]

Or

[tex]x^2 - 5x + 6 = 0[/tex]

Which is a quadratic equation with coefficients [tex]a = 1, b = -5, c = 6[/tex], and then:

[tex]\Delta = (-5)^{2} - 4(1)(6) = 1[/tex]

[tex]x_{1} = \frac{-(-5) + \sqrt{1}}{2} = 3[/tex]

[tex]x_{2} = \frac{-(-5) - \sqrt{1}}{2} = 2[/tex]  

Thus, the other two roots are [tex]x = 2[/tex] and [tex]x = 3[/tex].

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you answer is 5/8 please mark as brainliest if you need more help with questions like this lemme know

use the amount for each quantity to obtain theratio

choc chips : sugar = 5 : 3 = [tex]\frac{5}{3}[/tex]

Answer:

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

Step-by-step explanation:

To solve an absolute value equation of the form |X| = k, where X is an expression with a variable and k is a non-negative number or an expression, you must solve the compound equation X = k or X = -k.

The first step is to divide both sides by 9 to get the absolute value of an expression equal to a non-negative number.

9|9 – 8x| = 2x + 3

Divide both sides by 9.

[tex] |9 - 8x| = \dfrac{2x + 3}{9} [/tex]

Now we eliminate the absolute value by rewriting this as a compound equation.

[tex] 9 - 8x = \dfrac{2x + 3}{9} ~~~or~~~ 9 - 8x = -\dfrac{2x + 3}{9} [/tex]

We must solve both equations.

Multiply both sides by 9.

[tex] 9(9 - 8x) = 2x + 3 ~~~or~~~ 9(9 - 8x) = -(2x + 3) [/tex]

[tex] 81 - 72x = 2x + 3 ~~~or~~~ 81 - 72x = -2x - 3 [/tex]

[tex] -74x = -78 ~~~or~~~ -70x = -84 [/tex]

[tex] x = \dfrac{-78}{-74} ~~~or~~~ x = \dfrac{-84}{-70} [/tex]

[tex] x = \dfrac{39}{37} ~~~or~~~ x = \dfrac{6}{5} [/tex]

Answer: x = 39/37 or x = 6/5

To check for extraneous solutions, we plug in each solution into the original equation and check if it works.

Check 39/37:

9|9 – 8(39/37)| = 2(39/37) + 3

|81 - 72(39/37)| = 78/37 + 3

|2997/37 - 2808/37| = 78/37 + 111/37

|189/37| = 189/37

189/37 = 189/37

The solution 39/37 is valid.

Check x = 6/5.

9|9 – 8x| = 2x + 3

9|9 – 8(6/5)| = 2(6/5) + 3

|81 - 72(6/5)| = 12/5 + 15/5

|405/5 - 432/5| = 27/5

|-27/5| = 27/5

27/5 = 27/5

The solution x = 6/5 is also valid.

There are no extraneous solutions.

In this mathematical context, 'f' represents a vehicle's fuel efficiency in miles per gallon, and the given inequality f > 40 mpg indicates that the vehicle's fuel efficiency is higher than 40 miles per gallon.

The problem refers to a situation where a vehicle achieves fuel efficiency of more than 40 miles per gallon. This efficiency is quantified using the variable 'f'.

Considering f as the vehicle's fuel efficiency in miles per gallon, you are expressing a relationship where f > 40 mpg.

Using an example: if we consider a vehicle that achieves 43 miles per gallon, this can be represented as: f = 43 mpg. This efficiency is indeed more than 40 miles per gallon, thus confirming that f > 40 mpg in this case. It's important to understand that in this context, the fuel efficiency varies from one vehicle to another. For instance, vehicles become more fuel efficient over the years due to advancements in technology and heightened fuel economy standards.

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[tex]f(x)=2x-5,\ g(x)=x^2-4x-8\\\\(f+g)(x)=f(x)+g(x)=(2x-5)+(x^2-4x-8)\\\\=2x-5+x^2-4x-8=x^2+(2x-4x)+(-5-8)=x^2-2x-13[/tex]

Answer:

[tex]\text{The value of (f+g)(x) is }x^2-2x-13[/tex]

Step-by-step explanation:

Given the two functions

[tex]f(x)=2x-5[/tex]

[tex]g(x)=x^2-4x-8[/tex]

we have to find the value of (f+g)(x)

As we know

[tex](f+g)(x)=f(x)+g(x)=(2x-5)+(x^2-4x-8)[/tex]

[tex]=2x-5+x^2-4x-8[/tex]

[tex]=x^2+2x-4x-5-8=x^2-2x-13[/tex]

[tex]\text{Hence, the value of (f+g)(x) is }x^2-2x-13[/tex]

the answer to your question :[tex]4\sqrt{5}[/tex]

hope this helps! ❤ from peachimin

Exact Form:√5

Decimal Form:2.23606797…

d = r * t

                               time                rate                       distance

Downstream:           2                   8 + c                     d = 2(8 + c)

Upstream:                3                   8 - c                      d = 3(8 - c)

Since the distance is the same, we can set the distance equations equal to each other and solve for c.

2(8 + c) = 3(8 - c)

16 + 2c = 24 - 3c

16 + 5c = 24

      5c = 8

        c = [tex]\frac{8}{5}[/tex]

        c = 1.6

Answer: 1.6 mph

8,5 and 6,1

The slope is 2

y = | 3x - 7 |

x-intercept is when y = 0

0 = | 3x - 7 |

0 = 3x - 7

+7       +7

7 = 3x

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

 [tex]\frac{7}{3} = x[/tex]

[tex](\frac{7}{3}, 0 )[/tex]

y-intercept is when x = 0

y = | 3(0) - 7 |

y = | 0 - 7 |

y = | -7 |

y = 7

(0, 7)

Answer: [tex](\frac{7}{3}, 0 )[/tex] and (0, 7)

Step 1

Find the measure of angle x

we know that

If ray NP bisects <MNQ

then

m<MNQ=m<PNM+m<PNQ ------> equation A

and

m<PNM=m<PNQ -------> equation B

we have that

m<MNQ=(8x+12)°

m<PNQ=78°

so

substitute in equation A

(8x+12)=78+78-------> 8x+12=156------> 8x=156-12

8x=144------> x=18°

Step 2

Find the measure of angle y

we have

m<PNM=(3y-9)°

m<PNM=78°

so

3y-9=78------> 3y=87------> y=29°

therefore

the answer is

the measure of x is 18° and the measure of y is 29°

Answer: If NP bisects MNQ, MNQ=8x+12,PNQ=78, and RNM=3y-9, find the values of x and y

x= 18 y=11

Step-by-step explanation:

We know that MNQ= 8x+12

PNQ=78 and MNP is equal to PNQ

Therefore, PNQ=MNP

So since these two angles make up MNQ,

Add 78+78 which is 156

So now we need to find x

The equation to find x is 8x+12=156

8x+12=156

8x=144

x=18

Now that we know x it is time to find y.

So we know that RNM=3y-9

And we know that MNQ is equal to 156

RNM an MNQ form a straight line which means that it is equal to 180 degrees

So the equation to find y is 3y-9+156=180

3y-9+156=180

3y+147=180

3y=33

y=11

So in conclusion, x=18 and y=11

Hope this helped! :3

Answer:

Option B 0.11

Step-by-step explanation:

Given that  the population proportion of 0.58, a simulation of 200 trials is run, each with a sample size of 50 and a point estimate of 0.42. The minimum sample proportion from the simulation is 0.31, and the maximum sample proportion from the simulation is 0.53.

This gives an idea that confidence interval is

(0.31, 0.53) with mean being in the middle of this interval

Margin of error = 1/2 (length of this interval)

Length of confidence interval =[tex]0.53-0.31 =0.22[/tex]

Margin of error =± 1/2(0.22) = ±0.11

Hence option B is correct

[tex]g(x)=\dfrac{x-1}{4}\to y=\dfrac{x-1}{4}\\\\\text{change x to y and y to x}\\\\x=\dfrac{y-1}{4}\ \ \ \ |\text{solve for y}\\\\\dfrac{y-1}{4}=x\ \ \ \ \ |\cdot4\\\\y-1=4x\ \ \ \ |+1\\\\y=4x+1\\\\\boxed{g^{-1}(x)=4x+1}[/tex]

Given equation is [tex]x^3-5x^2+2x+6=0[/tex]

Usually we solve this type of problem by factoring but this equation is not factorable. If we solve by grouping then also we are not getting any common factor. So factoring method is not going to help. I this type of situation we may use graphing calculator. From graph we just need to pick those points where graph crosses the x-axis. Those values will be the final answer.

Using graphing calculator we see that there are three solutions at x=-0.856, x=1.678, x=4.177 which are approx x=-0.8, x=1.7 and x=4.2

Hence final answers are x=-0.8, x=1.7 and x=4.2.

Answer:

-0.9, 1.7, and 4.2

Step-by-step explanation:

[tex]E=\{-1,\ 0,\ 1,\ 2,\ 3,\ 4\}\\\\F=\{3,\ 4,\ 5,\ 6,\ 7,\ 8\}\\\\E\ \cup\ F=\{-1,\ 0,\ 1,\ 2,\ 3,\ 4,\ 5,\ 6,\ 7,\ 8\}[/tex]

All elements from set E and from the set F. The same elements are only once.

7×2=14e

7×1=7

14e-7-11=6+6e

   -6e             -6e

8e-7-11=6

    +7      +7

8e-11=13

     +11    +11

8e=24

8e÷8=e

24÷8=3

e=3

To solve the equation 7(2e-1)-11=6+6e for e, distribute, combine like terms, subtract, add, and divide until you have isolated e. The solution is e=3.

To solve for e in the equation 7(2e-1)-11=6+6e, first distribute the 7 on the left side of the equation:

14e - 7 - 11 = 6 + 6e

Now, combine like terms on both sides:

14e - 18 = 6 + 6e

Next, subtract 6e from both sides:

8e - 18 = 6

Add 18 to both sides:

8e = 24

Finally, divide by 8:

 e = 3.

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Answer:

[tex]\displaystyle \large{f\prime(x) = 2x \sin (x) + x^2 \cos (x)}[/tex]

Step-by-step explanation:

We are given a function:

[tex]\displaystyle \large{f(x) = x^2 \sin (x)}[/tex]

Notice that there are two functions multiplying each other. Recall the product rules.

[tex]\displaystyle \large{y=h(x)g(x) \to y\prime = h\prime (x) g(x) + h(x)g\prime (x)}[/tex]

You can let x^2 = h(x), sin(x) = g(x) or sin(x) = h(x), x^2 = g(x) as your desire but I’ll let h(x) = x^2 and g(x) = sin(x).

Therefore, from a function:

[tex]\displaystyle \large{f(x) = x^2 \sin (x) \to f\prime (x) = (x^2)\prime \sin(x) + x^2 (\sin (x))\prime}[/tex]

Recall the power rules and differentiation of sine.

[tex]\displaystyle \large{y = ax^n \to y\prime = nax^{n-1} \ \ \ \tt{for \ \ polynomial \ \ function}}\\ \displaystyle \large{y = \sin (x) \to y\prime = \cos (x) }[/tex]

Therefore, from differentiating function,

[tex]\displaystyle \large{f\prime(x) = 2x \sin (x) + x^2 \cos (x)}[/tex]

And we are done!

Hi, here is the solution.

The doubling each dimensions increases the volume by 8. That is (2 * 2* 2)

There 1000 toothpicks in a regular box.

The jumbo box hold  8 *1000 = 8000 toothpicks.

Thank you.