The equations of two lines are y=4x+2 and 6x-y=4 . What is the value of x in the solution for this system of equations?

Answer:

a) probability of choosing the mean amount of sleep for adult as  μ < 9 hours when it is μ = 8.5 hours is 0.4038

b) There is a 0.5962 probability of failing to choose that the mean amount of sleep for adult is  μ < 9 hours when it is μ = 8.5 hours

Step-by-step explanation:

a) Interpret the value of the power

The power of an hypothesis is the probability of rejecting the null hypothesis when the alternative hypothesis is valid. It is a type 1 error

Power = 0.4038

From the hypothesis test,

the null hypothesis, μ = 8.5 hours

Alternative hypothesis, μ < 9 hours

Sine the power is the probability of rejecting the null hypothesis, it means that the probability of choosing the mean amount of sleep for adult as  μ < 9 hours when it is μ = 8.5 hours is 0.4038

b)

Power + β = 1

β = 1 - Power

β = 1 - 0.4038

β = 0.5962

β, type 2 error, is the probability of not rejecting the null hypothesis even when it is false.

It means that there is a 0.5962 probability of failing to choose that the mean amount of sleep for adult is  μ < 9 hours when it is μ = 8.5 hours

The power of a test (0.4038 in this case) is the probability that we correctly reject the null hypothesis, given the actual population mean is 8.5 hours. Beta (1 - Power, or 0.5962 in this case) is the probability of committing a type II error, which is incorrectly accepting the null hypothesis.

In the context of hypothesis testing in statistics, the power of a test refers to the probability that the test will correctly reject the null hypothesis when the alternative hypothesis is true. In this specific scenario, the power of the test is 0.4038. This means that there is a 40.38% chance that we would correctly conclude that the mean sleep for adults is less than 9 hours, assuming that the actual population mean is 8.5 hours.

The value of beta represents the probability of committing a type II error, which is the error of not rejecting a null hypothesis when it should be rejected; in other words, incorrectly concluding that the mean sleep for adults is not less than 9 hours when it actually is. The value of beta can be calculated as 1 minus the power of the test, so in your case it would be 1 - 0.4038 = 0.5962. This means there is a 59.62% chance of committing a type II error.

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Answer:

The base is a square of side 9.19 cm and the height is 7.66 cm

[tex]C_m=126.58\ cents[/tex]

Step-by-step explanation:

Optimization

We'll use simple techniques to find the optimum values that minimize the cost function given in the problem. Since the restriction is an equality, the derivative will come handy to find the critical points and then we'll prove they are a minimum.

First, we consider the shape of the rectangular bin has a square base and no top. Let x be the side of the base, thus the Area of the base is

[tex]A_b=x^2[/tex]

Let y be the height of the box, thus each one of the four lateral sides of the box is a rectangle with sides x and y and the total lateral area is

[tex]A_s=4xy[/tex]

The cost of the material used to manufacture the box is 0.5 cents per square centimeter of the base and 0.3 cents per square centimeter of the sides, thus the total cost to produce one box is

[tex]C(x,y)=0.5x^2+0.3\cdot 4xy[/tex]

[tex]C(x,y)=0.5x^2+1.2xy[/tex]

Note the cost is a two-variable function. We need to have it expressed as a single variable function. To achieve that, we use the volume provided as [tex]646 cm^3[/tex]. The volume of the box is the base times the height

[tex]V=x^2y[/tex]

Using the value of the volume we have

[tex]x^2y=646[/tex]

Solving for y

[tex]\displaystyle y=\frac{646}{x^2}[/tex]

Replacing into the cost function, it only depends on one variable

[tex]\displaystyle C(x)=0.5x^2+1.2x\cdot \frac{646}{x^2}[/tex]

Operating

[tex]\displaystyle C(x)=0.5x^2+ \frac{775.2}{x}[/tex]

Taking the first derivative

[tex]\displaystyle C'(x)=x-\frac{775.2}{x^2}[/tex]

Equating to 0

[tex]\displaystyle x-\frac{775.2}{x^2}=0[/tex]

Solving

[tex]\displaystyle x=\sqrt[3]{775.2}[/tex]

[tex]x=9.19\ cm[/tex]

Now find the height

[tex]\displaystyle y=\frac{646}{9.19^2}[/tex]

[tex]y=7.66\ cm[/tex]

Find the second derivative

[tex]\displaystyle C''(x)=1+\frac{1550.4}{x^3}[/tex]

Since this value is positive, for all x positive, the function has a minimum at the critical point.

Thus, the minimum cost is

[tex]\displaystyle C_m=0.5\cdot 9.19^2+ \frac{775.2}{9.19}[/tex]

[tex]\boxed{C_m=126.58\ cents}[/tex]

Answer:

126.58 cents or $1.27

Step-by-step explanation:

the math from above is correct they just want the answers in dollars

Answer:

7.28 7.29  c

Step-by-step explanation:

The square root of 53 can be found to lie between the values of 7.28 and 7.29.

The square root function can only have non negative values. If we take thee square root of a number, we obtain a value that can be multiplied by itself to obtain the number.

The square root of 53 can be found to lie between the values of 7.28 and 7.29.

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Angle Zc measures 90° as it is supplementary to the given 90° angle. Therefore, Zc = 90°.

To find the measure of angle Zc, we need to use the properties of angles formed by intersecting lines.

Given:

- Angle Zc is supplementary to angle 90°.

- Angle 90° is formed by the intersection of lines, let's denote them as line AB and line CD.

- Angle 90° is bisected by line EF, forming two congruent angles.

Step-by-step explanation:

1. Since angle Zc is supplementary to angle 90°, we subtract the measure of angle 90° from 180° to find the measure of angle Zc.

  Measure of angle Zc = 180° - 90°

                                     = 90°

So, angle Zc measures 90°.

Answer:

A) f(x) = –16x2 + 99x + 6

Step-by-step explanation:

ed2021 :)

The correct value of the angle of rotation is 3π/5

Answer:

Distance travelled ≈ 22.6 ft

Step-by-step explanation:

We are given;

Radius;r = 12 ft

Angle of rotation; θ = 3π/5

The formula for calculating distance travelled is;

Distance travelled = rθ

So, plugging in the relevant values;

Distance travelled = 12 x 3π/5

Distance travelled ≈ 22.6 ft

Answer:

Probability that the spending is more than $42.35 is 0.7271.

Step-by-step explanation:

We are given that American Statistical Association budget is distributed normally with a mean spending of $45.67 and a standard deviation of $5.50.

Let X = American Statistical Association budget

So, X ~ N([tex]\mu=45.67,\sigma^{2} =5.5^{2}[/tex])

The z-score probability distribution for normal distribution is given by;

               Z = [tex]\frac{ X -\mu}{\sigma}[/tex]  ~ N(0,1)

where, [tex]\mu[/tex] = mean spending = $45.67

            [tex]\sigma[/tex] = standard deviation = $5.50

The Z-score measures how many standard deviations the measure is away from the mean. After finding the Z-score, we look at the z-score table and find the p-value (area) associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X.

So, the probability that the spending is more than $42.35 is given by = P(X > $42.35)

  P(X > $42.35) = P( [tex]\frac{ X -\mu}{\sigma}[/tex] > [tex]\frac{42.35-45.67}{5.5}[/tex] ) = P(Z > -0.604) = P(Z < 0.604)

                                                              = 0.7271

Now, in the z table the P(Z [tex]\leq[/tex] x) or P(Z < x) is given. So, the above probability is calculated by looking at the value of x = 0.604 in the z table which will lie between x = 0.60 and x = 0.70 which has an area of 0.7271.

Hence, the probability that the spending is more than $42.35 is 0.7271.

Answer:

A quadratic function can have two irrational roots.

A quadratic equation can have no real number solutions.

Step-by-step explanation:

A quadratic function can have two irrational roots.

A quadratic equation can have no real number solutions.

A quadratic function is a polynomial function with one or more in which highest exponent of variable is two.

According to the question,

A quadratic function can have two irrational roots.

example: [tex]x^{2} -2x -2 =0[/tex]

This equation have two irrational roots  1+√3 and 1 - √3.

A  quadratic function can have no real number solutions

Hence, A quadratic function can have two irrational roots.

A quadratic equation can have no real number solutions.

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Answer:

y = -2x+3

Step-by-step explanation:

Answer:

We have to produce the equation y = mx +b

We start by solving for b

b = y - mx

b = 3 - -2*0

b = 3

Let's put b and the slope into this equation

y = mx +b

y = -2*x +3

Step-by-step explanation:

Answer:

  -1

Step-by-step explanation:

The required relation is ...

  7n = n^2 -8

  0 = n^2 -7n -8 . . . . put in standard form

  0 = (n -8)(n +1) . . . . factor

Solutions are n=8 and n=-1.

The negative solution is -1.

Answer:

C

Step-by-step explanation:

A cube has 6 square faces

Each face: 5² = 25

Surface area: 6(25) = 150 in²

Answer:

[tex]f(a) = \frac{(a+5)}{(a-1)}[/tex]

Step-by-step explanation:

Given : [tex]f(x) = \frac{(3+x)}{(x-3)}[/tex]

In order to find [tex]f(a+2)[/tex] we will substitute [tex](a+2)[/tex] for [tex]x[/tex] in the given function, that is :

[tex]f(a) = \frac{(3+a+2)}{(a+2-3)}[/tex]

[tex]f(a) = \frac{(a+5)}{(a-1)}[/tex]

Answer:

Probability that the person preferred milk as his or her primary drink  = 0.3

Step-by-step explanation:

Given -

In a recent survey, 18 people preferred milk, 29 people preferred coffee, and 13 people preferred juice as their primary drink for breakfast .

Total no of people is =  18 + 29 + 13 = 60

If a person is selected at random ,

The probability of person preferred milk = [tex]\frac{18}{60}[/tex]

The probability of person preferred coffee = [tex]\frac{29}{60}[/tex]

The probability of person preferred juice = [tex]\frac{13}{60}[/tex]

Probability that the person preferred milk as his or her primary drink =

P ( milk ) = [tex]\mathbf{\frac{No\;of\;favourable\;outcomes}{total\;no\;of\:outcomes}}[/tex]

    =   [tex]\frac{18}{60}[/tex]  =  0.3

Answer:

a

Step-by-step explanation:

a yard is 3 feet.24/3 equals 8 .then 80!

Answer:

C 66 miles

Step-by-step explanation:

88miles/4 gallons = 22 miles/gallon

22 miles/ gallon * 3 gallons = 66 miles

Answer:

66 miles per 3 gallons

Step-by-step explanation:

if you divide 88 by 4 you get 22 which means you get 22 miles to each gallon so for three gallons you would be able to drive 66 miles

Hope I helped:)

Answer:

7/12

Step-by-step explanation:

Probability is a ratio defined by the number of possible outcome to the number of total outcome. The probability that an event will happen added to the probability that the event will not happen gives 1. In other words, the outcome of a probability cannot exceed 1.

The probability that an event a will happen or that another independent event  b will happen is the sum of the probability that a will happen to the probability that b will happen.

For the 2 dies, the outcomes possible when rolled are as shown below  

O   1     2     3    4    5     6

1    2    3     4     5    6    7

2   3    4     5    6    7     8

3   4    5    6    7      8    9

4   5    6    7     8    9    10

5   6     7   8    9    10    11

6   7    8    9    10    11    12    

From the table, there are 36 possible outcomes but only 21 outcomes are less than 8 hence the probability required

= 21/36

= 7/12      

Answer:

5 laps

Step-by-step explanation:

We can use ratios to solve

3 minutes        15 minutes

----------------- = ------------------------

1 lap                   x laps

Using cross products

3x = 15

Divide each side by 3

3x/3 = 15/3

x = 5

He can do 5 laps

Answer:

I hope this helps

Answer:

Step-by-step explanation:

Hello!

According to a study regarding the average age of female and male kids to complete toilet training is:

Females:

Average age 32.5 months

The standard deviation of 6.7 months

n= 126

Males:

Average age 35.0 months

The standard deviation of 10.1 months

n= 141

The parameter of study is the difference between the age of females are successfully toilet trained and the average age that males are successfully toilet trained. μf - μm (f= female and m= male)

a.

Assuming that both variables have a normal distribution to choose whether you'll use an unpooled or pooled-t to calculate the confidence interval you have to conduct an F-test for variance homogeneity.

If the variances are equal, then you can usee the pooled-t, but if the variances are different, you have to uses Wlche's approach:

H₀: δ²f = δ²m

H₁: δ²f ≠ δ²m

Since both items b. and c. ask for a 95% CI I'll use the complementary significance level for this test:

α: 0.05

[tex]F= \frac{S^2_f}{S^2_m} * \frac{xSigma^2_f}{Sigma^2_m} ~~~F_{(n_f-1); (n_m-1)}[/tex]

[tex]F= \frac{(6.7^2)}{(10.1)^2} *1= 0.44[/tex]

Critical values:

[tex]F_{125;140;0.025}= 0.71\\F_{125;140;0.975}= 1.41[/tex]

The calculated F value is less than the lower critical value, 0.77, so the decision is to reject the null hypothesis. In other words, there is no significant evidence to conclude the population variances of the age kids are toilet trained to be equal. You should use Welch's approach to construct the Confidence Intervals.

[tex]Df_w= \frac{(\frac{S^2_f}{n_f} + \frac{S^2_m}{n_m} )^2}{\frac{(\frac{S^2_f}{n_f} )^2}{n_f-1} +\frac{(\frac{S^2_m}{n_m} )^2}{n_m-1} }[/tex]

[tex]Df_w= \frac{(\frac{6.7^2}{126} + \frac{10.1^2_m}{141} )^2}{\frac{(\frac{126^2}{126} )^2}{126-1} +\frac{(\frac{10.1^2}{141} )^2}{141-1} } = 254.32[/tex]

b.

The given interval is:

[0.3627; 4.6073]

Using Welch's approach, the formula for the CI is:

(X[bar]f- X[bar]m) ± [tex]t_{Df_w;1-\alpha /2}[/tex] * [tex]\sqrt{\frac{S^2_f}{n_f} +\frac{S^2_m}{n_m} }[/tex]

or

(X[bar]m- X[bar]f) ± [tex]t_{Df_w;1-\alpha /2}[/tex] * [tex]\sqrt{\frac{S^2_f}{n_f} +\frac{S^2_m}{n_m} }[/tex]

As you can see either way you calculate the interval, it is centered in the difference between the two sample means, so you can clear the value of that difference by:

(Upper bond - Lower bond)/2= (4.6073-0.3627)/2= 2.1223

The average age for females is 32.5 months and for males, it is 35 months.

Since the difference between the sample means is positive, we can say that the boys were considered "group 1" and the girls were considered "group 2"

You have a95% confidence that the parameter of interest is included in the given confidence interval.

c.

None of the statements is correct, the interval gives you information about the difference between the average age the kids are toilet trained, that is between the expected ages for the entire population of male and female babies.

This represents a guideline but is not necessarily true to all individuals of the population since some male babies can be toilet trained before that is expected as some female babies can be toiled trained after the average value.

I hope it helps!

Answer:

P(X>17) = 0.979

Step-by-step explanation:

Probability that a camera is defective, p = 3% = 3/100 = 0.03

20 cameras were randomly selected.i.e sample size, n = 20

Probability that a camera is working, q = 1 - p = 1 - 0.03 = 0.97

Probability that more than 17 cameras are working P ( X > 17)

This is a binomial distribution P(X = r) [tex]nCr q^{r} p^{n-r}[/tex]

[tex]nCr = \frac{n!}{(n-r)!r!}[/tex]

P(X>17) = P(X=18) + P(X=19) + P(X=20)

P(X=18) = [tex]20C18 * 0.97^{18} * 0.03^{20-18}[/tex]

P(X=18) = [tex]20C18 * 0.97^{18} * 0.03^{2}[/tex]

P(X=18) = 0.0988

P(X=19) = [tex]20C19 * 0.97^{19} * 0.03^{20-19}[/tex]

P(X=19) = [tex]20C19 * 0.97^{19} * 0.03^{1}[/tex]

P(X=19) = 0.3364

P(X=20) = [tex]20C20 * 0.97^{20} * 0.03^{20-20}[/tex]

P(X=20) = [tex]20C20 * 0.97^{20} * 0.03^{0}[/tex]

P(X=20) = 0.5438

P(X>17) = 0.0988 + 0.3364 + 0.5438

P(X>17) = 0.979

The probability that there are more than 17 working cameras should be 0.979 for the company to accept the whole batch

Answer:Y=0 Y=-3

Step-by-step explanation:

Answer:

First graph y=0

Second graph y=-3

Step-by-step explanation:

Edge 2022

Answer:??

Step-by-step explanation:

Answer: dont have an answer

Step-by-step explanation:

sorry

Answer:

wydjae  is męi ze tak

Step-by-step explanation:

The appropriate scale for the y-axis include:

A = 2000

B = 4000

C = 6000

D = 8000

E = 10000

F = 12000

G = 14000

In Mathematics and Euclidean Geometry, a bar chart is a type of graph that is used for the graphical representation of a data set, especially through the use of rectangular bars and vertical columns.

Since the set of axes starts from the origin (0, 0), an appropriate scale for the y-axis (number of satisfied customers) of the graph can be calculated as follows;

1 unit = 250 customers

4 units = (4 × 250) = 2,000 customers.

In this context, the appropriate scale for the y-axis should be completed as follows:

A = 2000

B = 4000

C = 6000

D = 8000

E = 10000

F = 12000

G = 14000

Complete Question;

Look at chart below.

The number of satisfied customers is given below each month on the x-axis.

Select an appropriate scale for the y-axis of the graph.

The appropriate scale for the y-axis is:

A =

B =

C =

D =

E =

F =

G =

Answer:

Step-by-step explanation:

Given that,

A rectangular prism with a volume of 8 cubic units, V = 8 cubic units

The rectangular prism is filled with a cube twice.

First one

A cube with ½ length unit, we should know that a cube have equal length

Then, L = ½ units

Volume of a cube is L³

V = L³

V1 = (½)³ = ⅛ cubic units

Second cube

A cube with ⅓ length unit, we should know that a cube have equal length

Then, L = ⅓ units

Volume of a cube is L³

V = L³

V1 = (⅓)³ = 1 / 27 cubic units

So, to know number of times cube one will filled the rectangular prism

V = nV1

Where V is the volume of rectangular prism

n is the number of times the cube will be able to matched up with the volume of the rectangular prism

Then, n_1 = V / V1

n_1 = 8 / ⅛

n_1 = 64 times

Also,

n_2 = V / V2

n_2 = 8 / 1 / 27

n_2 = 8 × 27 = 216 times

So, the we need more of ⅓units and we will need (216 - 64) = 152 times

We need 152 more of ⅓units

You need 152 more cubes with side lengths of 1/3 unit than cubes with side lengths of 1/2 unit to fill a rectangular prism with a volume of 8 cubic units.

To determine how many more cubes with side lengths of 1/3 unit are needed to fill the rectangular prism compared to cubes with side lengths of 1/2 unit, we first need to find the number of each type of cube that fits into the prism.

The volume of the rectangular prism is given as 8 cubic units.

First, let's calculate the volume of one small cube:

Next, determine how many of each type of cube are needed to fill the prism:

The difference in the number of cubes needed is:

216 (1/3-unit cubes) - 64 (1/2-unit cubes) = 152 more 1/3-unit cubes.

Answer:

0.8937

Step-by-step explanation:

This is a case of binomial probability with n = 64, p = 0.10 and x = 3.  This means that the probability of a cancellation is 10%.  Here, we can find the probability that more than 3 cancellations or no shows will occur by finding binompdf(64,0.10, 0) + binompdf(64,0.10, 1) + binompdf(64,0.10, 2) + binompdf(64,0.10, 3) and then subtracting this sum from 1.000.  

We get:    0.0012 + 0.0084 + 0.0293 + 0.0674 = sum = 0.1063

Then the desired probability is 1.0000 - 0.1063 = 0.8937

The probability that more than 3 cancellations and/or no-shows will occur during the next week is: 0.8937

This involves binomial probability distribution with the formula;

P(X = x) = ⁿCₓ × pˣ × q⁽ⁿ ⁻ ˣ⁾

We are given;

p = 10% = 0.1

n = 64

q = 1 - p = 1 - 0.1

q = 0.9

We want to find the probability that more than 3 cancellations and/or no-shows will occur during the next week is given by;

P(X > 3) = 1 - (P(X = 0) + P(X = 1) + P(X = 2) + P(X =3))

From online binomial probability calculator;

P(0) = 0.0012

P(1) = 0.0084

P(2) = 0.0293

P(3) = 0.0674

Thus;

P(X > 3) = 1 - (0.0012 + 0.0084 + 0.0293 + 0.0674 )

P(X > 3) = 1 - 0.1063

P(X > 3) = 0.8937

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Answer:

Step-by-step explanation:

The answer is 10 bananas and 2 apples

The number of apples are 2 and number of bananas is 10.

Two or more expressions with an Equal sign is called as Equation.

Given that Hattie is making fruit baskets, which includes apples and bananas, to send to some of her real estate clients.

She wants each basket to have 12 pieces of fruit, but the fruit should weigh no more than 80 ounces total.

On average, each apple weighs 5 ounces, and each banana weighs 7 ounces.

Let Bananas is denoted by B and Apples are represented by A.

A+B=12...(1)

5A+7B<80...(2)

A=12-B

Substitute in equation 2.

5(12-B)+7B=80

60-5B+7B=80

60+2B=80

Subtract 60 on both sides.

2B=80-60

2B=20

Divide both sides by 2.

B=10

A+B=12

A+10=12

A=2

Hence, the number of apples are 2 and number of bananas is 10.

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Answer:

you are to subtract the equation

Answer:

(7,-8)

Step-by-step explanation:

Answer:

We have,

max 4x+10y

3x+4y<480

4x+2y<360

The feasible corner points are ( 48,84),(0,120),(0,0),(90,0)

Now, our problem is maximum type so put above feasible points in equation max 4x + 10y one by one and select one point at which our value from this equation is maximum,

(48,84) 4*48+10*84 1032

(0,120) 4*0+10*120 1200

(0,0) 4*0+10*0 0

(90,0) 4*90+10*0 360

Here we get maximum value at (0,120) which is 1200.

Correct option is (B)1200

Answer:

Answer is 1200.

Refer below.

Step-by-step explanation:

The maximum possible value for the objective function is 1200.