Solve system of equations.
-3 x-y=4
4 x+2 y=-8

Answer:

\(\displaystyle g(f(1)) = 20\)

Step-by-step explanation:

We are given the two functions:

\(f(x)=6x+2 \text{ and } g(x)=2x+4\)

And we want to find:

\(g(f(1))\)

First, find f(1):

\(\displaystyle \begin{aligned} f(1) &= 6(1) + 2 \\ &= 6 + 2 \\ &= 8 \end{aligned}\)

Substitute:

\(g(f(1))=g(8)\)

Find g(8):

\(\displaystyle \begin{aligned} g(8) &= 2(8) + 4 \\ &= 16 + 4 \\ &= 20 \end{aligned}\)

In conclusion:

\(\displaystyle g(f(1)) = 20\)

Answer:

Vertices = 8

Edges = 12

Faces = 6

Step-by-step explanation:

A cuboid ( or a rectangular solid ) has 8 vertices , 12 edges & 6 faces.

The eye color of people on commercial aircraft flights is not a random variable.

What is random variable?

Random variables are variables that can take on different values based on the outcome of a random event or experiment.

However, eye color is a characteristic of individuals and does not vary randomly within a specific context, such as being on a commercial aircraft flight. Eye color is determined by genetic factors and does not change during a flight or as a result of being on a flight.

Eye color is a categorical variable that represents the color of an individual's eyes, such as blue, green, brown, or hazel. While it is not a random variable in the context of commercial aircraft flights, it can still be observed and recorded as a characteristic of the passengers on the flight.

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Approximately 34% of American adults have a mobile phone but not a landline, based on the given proportions from the study conducted by the Centers for Disease Control.

The proportion of American adults who have a mobile phone but not a landline, we need to subtract the proportion of those who have both a mobile phone and a landline from the proportion of those who have a mobile phone.

Let's denote the proportion of American adults who have a mobile phone as P(M), the proportion who have a landline as P(L), and the proportion who have neither as P(N).

Given information:

P(M) = 89% (proportion with a mobile phone)

P(L) = 57% (proportion with a landline)

P(N) = 2% (proportion with neither)

We can now calculate the proportion of adults who have a mobile phone but not a landline using the following equation:

P(M and not L) = P(M) - P(M and L)

To find P(M and L), we can subtract P(N) from P(L) since those who have neither are not included in the group with a landline:

P(M and L) = P(L) - P(N)

P(M and L) = 57% - 2%

P(M and L) = 55%

Now we can substitute the values back into the equation to find P(M and not L):

P(M and not L) = P(M) - P(M and L)

P(M and not L) = 89% - 55%

P(M and not L) = 34%

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Answer:  The total number of colored papers is 18.

Step-by-step explanation:

Given: The ratio of coloured papers to wight papers is 3:8.

Let total number of colored papers = 3x

and total number of wight papers = 8x

Since, there are 48 wight papers , then

\(8x=48\)

\(\Rightarrow\ x=6\)

Now , number of colored papers = 3(6)=18

Hence, the total number of colored papers is 18.

Answer:

6 seconds

Step-by-step explanation:

The object started at about 600 feet above the ground at 0 seconds.

The graph shows the object is shown on the graph being at zero at 6 seconds.

Thrust bearings are rotary bearings that allow the rotation of machine components relative to each other while transmitting loads and reducing friction. They are used in steam turbines, hydro turbines, pumps, gearboxes, etc. and carry loads that are perpendicular to the shaft axis.

Thrust bearings carry loads that are perpendicular to the axis of the shaft. A thrust bearing is a type of rotary bearing. It allows the rotation of machine components relative to each other while transmitting loads and reducing friction. Thrust bearings are designed to accommodate axial loads and are often located in applications where axial loads are transmitted from one part to another.

Thrust bearings may be used to accommodate loads that are parallel to the shaft axis, at an angle to the shaft axis, or perpendicular to the shaft axis. The application of thrust bearings can be observed in steam turbines, hydro turbines, pumps, gearboxes, etc.

Thrust bearings carry loads that are perpendicular to the axis of the shaft. This means that the loads exerted on the bearing are perpendicular to the direction of rotation of the shaft. The bearing is designed to accommodate these loads and transmit them to the surrounding structure without damaging the bearing or other components. Therefore, option C is correct, i.e., thrust bearings carry loads that are perpendicular to the axis of the shaft.

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Answer:  c

Step-by-step explanation:

The value of cv1, the lower critical value, is approximately 54.19.

To find the critical value (cv1) for a two-tailed hypothesis test at a 10% significance level, we need to divide the significance level (α) by 2.

Since α = 0.10, we divide it by 2 to get 0.10/2 = 0.05.

Next, we need to find the z-score associated with the cumulative probability of 0.05.

Using a standard normal distribution table or a calculator, we can find that the z-score for a cumulative probability of 0.05 is approximately -1.645.

Now, we can calculate the critical value by multiplying the z-score by the standard deviation (27) and adding it to the population mean (100).

cv1 = 100 + (-1.645 * 27)
cv1 ≈ 54.19 (rounded to two decimal places)

Therefore, the value of cv1, the lower critical value, is approximately 54.19.

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the control limits for the x-bar chart are 9.7439 minutes (LCL) and 11.0561 minutes (UCL), and the control limits for the R chart are 0 minutes (LCL) and 2.0529 minutes (UCL).

To compute the control limits for the x-bar (mean) and R (range) charts, we'll use the following formulas:

For the x-bar chart:

Upper Control Limit (UCL) for x-bar = x-double-bar + A2 * R-bar

Lower Control Limit (LCL) for x-bar = x-double-bar - A2 * R-bar

For the R chart:

Upper Control Limit (UCL) for R = D4 * R-bar

Lower Control Limit (LCL) for R = D3 * R-bar

Where:

x-double-bar = Overall mean of the sample means

R-bar = Overall mean of the sample ranges

A2 = Constant from the control chart constants table

D4 = Constant from the control chart constants table

D3 = Constant from the control chart constants table

For sample sizes of 4, the control chart constants are as follows:

A2 = 0.729

D4 = 2.281

D3 = 0

Given the information you provided:

Overall mean (x-double-bar) = 10.4 minutes

Average range (R-bar) = 0.9 minutes

Let's calculate the control limits:

For the x-bar chart:

UCL for x-bar = 10.4 + 0.729 * 0.9

             = 10.4 + 0.6561

             = 11.0561 minutes

LCL for x-bar = 10.4 - 0.729 * 0.9

             = 10.4 - 0.6561

             = 9.7439 minutes

For the R chart:

UCL for R = 2.281 * 0.9

         = 2.0529 minutes

LCL for R = 0

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0.688 will be the probability of getting a nickel from the jar.

Given,

Probability;-

Simply put, probability is the likelihood that something will occur. When we don't know how an event will turn out, we can discuss the likelihood or likelihood of several outcomes. Statistics is the study of events that follow a probability distribution.

Here,

The number of fortunate situations divided by the total number of coins would be the product between the probability of each occurrence and the likelihood of each event.

Therefore,

P(nickel) = 19/69

P(penny) = 17/68

That is,

P = 19/69 × 17/68

P = 323/4692

P = 0.0688

That is,

The probability of getting nickel from the jar is 0.06888

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Answer:

\( 48 - 20x = 9 \)

Step-by-step explanation:

\( 2 - \dfrac{5}{6}x = \dfrac{3}{8} \)

Multiply both sides by the LCD which is 24.

\( 24(2 - \dfrac{5}{6}x) = 24(\dfrac{3}{8}) \)

\( 48 - 20x = 9 \)

Answer:

Step-by-step explanation:

18. m∠1 = 104°

19. m∠2 = 79°

20. m∠3 = 65°

21. m∠5 = 73°

Bread is usually fine to eat if you don't see any mold.

Once refrigerated, it will retain its freshness for three to four days before becoming stale. If you want to extend its shelf life, packaged bread will stay fresh for at least three months in the freezer. If you do see mold, however, throw the bread out.

Answer:

0.16

Step-by-step explanation:

Answer:

1/6 serving

Step-by-step explanation:

1 SERVING = 3/2 OUNCES

        x        = 1/4 OUNCES

CROSS MULTIPLY.

1 * 1/4 ( serving * ounces) = x * 3/2 (ounces)

REARRANGE, THEN DIVIDE BOTH SIDES BY 3/2 OUNCES TO MAKE x THE SUBJECT.

x * 3/2 (ounces) = 1 * 1/4 ( serving * ounces)

[x * 3/2 (ounces)] / 3/2 OUNCES = [1 * 1/4 ( serving * ounces)] / 3/2 OUNCES

x = (1/4) / (3/2) SERVING

x = 1/4 * 2/3 (serving)

x = 1/2 * 1/3 (serving)

x = 1/6 serving

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Answer:

Three solutions were found :

x = 3/2 = 1.500

x = 2

x = -1

Step-by-step explanation:

Answer:

Option a: m ≠ 0

Step-by-step explanation:

After a small online search, I've found that the complete question is:

If the function f(x) = m*x + b has an inverse function, which statement must be true?

a) m ≠ 0

b) m = 0

c) b ≠ 0

d) b = 0

Ok, if g(x) is an inverse of the function f(x), then:

g( f(x)) = x

f( g(x)) = x

Let's assume that f(x) = m*x + b  has an inverse, and this inverse function is g(x).

Because f(x) is linear, g(x) is also linear, then:

g(x) = n*x + c

Let's find the values of A and B.

We know that:

f( g(x)) = x =  m*(n*x + c) + b

then

x = m*n*x + m*c + b

Then we must have:

m*n = 1

(m*c + b)  = 0

From the first equation m*n = 1

We get:

n = 1/m

The slope of the inverse function is one over the slope of the original function.

Because m is on the denominator, m can not be equal to zero (because a division by zero is not defined)

Then the correct option is the option a, m ≠ 0.          

Answer:

A

Step-by-step explanation:

edge 2021

The correct statement is that the solution to an absolute value equation must always be greater than or equal to zero. The absolute value of a number is its distance from zero on the number line. Thus, the absolute value of any number is always greater than or equal to zero.

The correct option is-C

The absolute value of a negative number is its opposite, which is always positive. The absolute value of a positive number is the same number.To solve an absolute value equation, you must isolate the absolute value first, then write two equations using the positive and negative versions of the absolute value expression. You can then solve for the variable in each equation to obtain two solutions. Therefore, not every absolute value equation has two solutions. It's possible for an absolute value equation to have one solution as well as no solution.

Additionally, the solutions to an absolute value equation can be negative as well. In summary, data markers are used in charts to represent individual data points. They are often used in combination with other chart elements, such as axes, gridlines, and legends, to help viewers understand the data being presented. The column, bar, area, dot, pie slice, or other symbol in a chart that represents a single data point is a data marker. Data markers provide you with a visual representation of the data in a chart. For example, in a column chart, each column represents a single data point.

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In a standard normal distribution, the mean is 0 and the standard deviation is 1.

Then, according to the normal table, the probability of gettin z < 0.18 is given by the area on the left of z = 0.18 in the graph related to the distribution. Then we have: P (z < 0.18) = 0.5714

Answer:

68°/•

Step-by-step explanation:

100°/• - 32°/•

=68°/•

Answer:

7. 49

8. -135

9. -96

10. 300

11. 0

12. -192

The perpendicular height of the cone, when its radius is 11 cm and the volume is 450 cm³, is approximately 11.15 cm (rounded to 1 decimal place).

To find the perpendicular height of the cone, we can use the formula for the volume of a cone, which is given by:

Volume = (1/3) * π * r^2 * h,

where r is the radius of the cone's base and h is the perpendicular height.

Given that the volume of the cone is 450 cm³ and the radius is 11 cm, we can substitute these values into the formula and solve for h.

450 cm³ = (1/3) * π * (11 cm)^2 * h

To solve for h, we can isolate it by dividing both sides of the equation by [(1/3) * π * (11 cm)^2]:

h = (450 cm³) / [(1/3) * π * (11 cm)^2]

Simplifying further:

h = (450 cm³) / [(1/3) * 121π cm²]

h = (450 cm³) / [40.333... cm²]

h ≈ 11.15 cm (rounded to 1 decimal place)

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The value of the expression according to the order of operations is -11. Thus option D is correct.

According to the statement

We have to find that the value of the given expression.

So, For this purpose, we know that the

The order of operations is a rule that tells the correct sequence of steps for evaluating a math expression.

From the given information:

The expression are :

(-2)-3-6

Now solve it with the order then

(-2)-3-6 = (-2)-3-6

(-2)-3-6 = -2-3-6

Now add the first two terms

then

(-2)-3-6 = -5-6

Now, Add next two terms

Then

(-2)-3-6 = -11.

The value becomes -11.

So, The value of the expression according to the order of operations is -11. Thus option D is correct.

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Answer:

165

Step-by-step explanation:

What this ratio means is that for every 2 white carnations, there is 1 blue and 3 red.

We have 60 white, or 30 groups of 2

We have 3 red carnations for each group of two:

3 * 30 = 90

And we have 1 blue for each group of two:

30 / 2 = 15

So, our total number of carnations would be 90 + 15 + 60

Or: 165

Answer: Rachel's prediction is faster than the actual unit rate, and Theadore's prediction is slower.

Answer:

I'm pretty positive the answer is B

Step-by-step explanation:

Since it's been 7 1/2 weeks and they thought it would grow atleast 2/5 a foot a week that should mean it's growing faster than anticipated.