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1 year ago

Use the drop-down menus to choose steps in order to correctly solve 4k−6=-2k−16−2 for k .

1 answer:

8 0

While there is no drop-down menu options for me to choose. I will show you how to solve this.

$\mathrm{Subtract\:the\:numbers:}\:-16-2=-18 \ \textgreater \ 4k-6=-2k-18$

$\mathrm{Add\:}6\mathrm{\:to\:both\:sides} \ \textgreater \ 4k-6+6=-2k-18+6 \ \textgreater \ Simplify$

$4k=-2k-12 \ \textgreater \ \mathrm{Add\:}2k\mathrm{\:to\:both\:sides} \ \textgreater \ 4k+2k=-2k-12+2k$

Simplify again.

$6k=-12 \ \textgreater \ \mathrm{Divide\:both\:sides\:by\:}6 \ \textgreater \ \frac{6k}{6}=\frac{-12}{6} \ \textgreater \ Simplify \ \textgreater \ k=-2$

Hope this helps!

You might be interested in

What are the coordinates of the circumcenter of this triangle? Enter your answer in the boxes.

Juliette [100K]

Answer:

(2,1)

Step-by-step explanation:

We can see that the given triangle.

The coordinates of A are (-1,5) .

The coordinates of B are (-1,-3).

The coordinates of C are (5,-3).

Distance formula: $\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}$

AB= $\sqrt{(-3-5)^2+(-1+1)^2}=8$ units

BC= $\sqrt{(5+1)^2+(-3+3)^2}=6$ units

AC= $\sqrt{(5+1)^2+(-3-5)^2}=10$ units

Pythagoras theorem: $(Hypotenuse)^2=(Base)^2+(Perpendicular\;side)^2}$

$AB^2+BC^2=8^2+6^2=100$

$AC^2=(10)^2=100$

Therefore, $AC^2=AB^2+BC^2$

When a triangle satisfied the Pythagoras theorem then, the triangle is right triangle.

Hence, the given triangle is a right triangle.

We know that circum-center of right triangle is the mid point of hypotenuse.

Mid-point formula: $x=\frac{x_1+x_2}{2},y=\frac{y_1+y_2}{2}$

Using this formula then, we get

Mid-point of hypotenuse AC is given by

$x=\frac{-1+5}{2}=2,y=\frac{5-3}{2}=1$

Hence, the circum-center of triangle is (2,1).

7 0

2 years ago

Triangle A and triangle B are drawn on the grid. Describe fully the single transformation which maps triangle A onto triangle B.

madam [21]

Answer:

Step-by-step explanation:

Triangle A, transforms into a smaler size, and goes into full shape. Triangle B, goes into the negative numbers.

7 0

1 year ago

How much money do winners go home with from the television quiz show Jeopardy? To determine an answer, a random sample of winner

Liula [17]

Answer:

The 95% confidence interval would be given by (14444.04;33657.30)

Step-by-step explanation:

Previous concepts

A confidence interval is "a range of values that’s likely to include a population value with a certain degree of confidence. It is often expressed a % whereby a population means lies between an upper and lower interval".

The margin of error is the range of values below and above the sample statistic in a confidence interval.

Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".

Data: $26,650 $6,060 $52,820 $8,490 $13,660$25,840 $49,840 $23,790 $51,480 $18,960$990 $11,450 $41,810 $21,060 $7,860

We can calculate the mean and the deviation from these data with the following formulas:

$\bar X= \frac{\sum_{i=1}^n x_i}{n}$

$s=\sqrt{\frac{\sum_{i=1}^n (x_i -\bar X)^2}{n-1}}$

$\bar X=24050.67$ represent the sample mean for the sample

$\mu$ population mean (variable of interest)

s=17386.13 represent the sample standard deviation

n=15 represent the sample size

The confidence interval for the mean is given by the following formula:

$\bar X \pm t_{\alpha/2}\frac{s}{\sqrt{n}}$ (1)

In order to calculate the critical value $t_{\alpha/2}$ we need to find first the degrees of freedom, given by:

$df=n-1=15-1=14$

Since the Confidence is 0.95 or 95%, the value of $\alpha=0.05$ and $\alpha/2 =0.025$ , and we can use excel, a calculator or a tabel to find the critical value. The excel command would be: "=-T.INV(0.025,14)".And we see that $t_{\alpha/2}=2.14$

Now we have everything in order to replace into formula (1):

$24050.67-2.14\frac{17386.13}{\sqrt{15}}=14444.04$

$24050.67+2.14\frac{17386.13}{\sqrt{15}}=33657.30$

So on this case the 95% confidence interval would be given by (14444.04;33657.30)

6 0

2 years ago

Emily went to the movie theater for her birthday. A mix of adults and children attended, making a total of 22 people. Each adult

viktelen [127]

Answer:

13 children and 9 adults if the total cost is $152.5

Step-by-step explanation:

Let x children and y adults

x + y = 22 (1)

5.5x + 9y = 125.5 (2)

y = 22 - x

5.5x + 9(22 - x) = 125.5

5.5x + 198 - 9x = 125.5

-3.5x = 125.5 - 198

-3.5x = -72.5

x = 20.7

y = 22 - x = 1.3

Which is not possible

If the total cost is $152.5

x + y = 22 (1)

5.5x + 9y = 152.5 (2)

y = 22 - x

5.5x + 9(22 - x) = 152.5

5.5x + 198 - 9x = 152.5

-3.5x = 152.5 - 198

-3.5x = -45.5

x = 13

y = 22 - 13 = 9

3 0

2 years ago

To increase sales, a local donut shop began putting an extra donut in some of the boxes. Customers are unaware of which boxes ha

Bingel [31]

Answer:

Step-by-step explanation:

Hello!

Part A

First, determine your study variable:

X: Number of boxes with an extra donut in a sample of eight.

To see if the variable has a Binomial distribution you have to check if the binomial criteria are met:

1. The number of observation of the trial is fixed (In this case n = 8, the boxes each customer bought make the sample)

2. Each observation in the trial is independent, this means that none of the trials will affect the probability of the next trial (In this case, the amount of donuts in one box does not affect on the probability of the next box having an extra donut)

3. The probability of success in the same from one trial to another (In this case our "success" will be that the box has an extra donut, according to the owners claim that is 1/7; ρ=0,14)

So X≈ Bi (n;ρ)

Where n represents the sample (n=8) and ρ is the probability of success (ρ=0.14)

Part B

The mean of the binomial distribution is E(X)= nρ

E(X)= 8 * 0.14= 1.12

The mean of the distribution is also called the expected value. You'd expect that 1.12 boxes have an extra donut.

The variance of the binomial distribution is V(X)= nρ(1 - ρ)

V(X)= 8*0.14*(1 - 0.14)= 0.9632

Its square root is the standard deviation

√V(X)= 0.98

The standard deviation is a measure of dispersion, it indicates how much the values of the distribution of the central value are separated. In this case, 0.98 indicates that the distribution of the number of boxes with an extra donut is far from the expected value.

Part C

Two of the eight customers buy a box with an extra donut, symbolically:

P(X=2) = P(X≤2) - P(X≤1)= 0.91 - 0.68 = 0.22

There is a 22% chance that two customers bought a box with an extra donut.

Compute:

P(X≥2)= 1 - P(X<2)= 1 - P(X≤1)= 1 - 0.68= 0.32

There is a 32% chance that two or more customers bought a box with an extra donnut.

I hope it helps!

3 0

1 year ago