Please explain how to find 40 x 50 using mental math... xD

F(5)= 3.(5)+2=15+2=17

Another example: F(0)=3.(0)+2=0+2=2

You just replace the value in the two sides.

Answer:

1.) x=2y-4

2.) x=2y-4 :)

Answer:

\(3x - 6y = - 12 ..........i)\\ x - 2y = - 8............ii) \\ x = 2y - 8 \\ Substituting \: the \: value \: of \: x \:in \: equation \: i) \: we \: get \\ 3(2y - 8) - 6y = - 12 \\ 6y - 24 - 6y = - 12 \\ Here \: we \: can \: see \:that\: the \: value \: of \: y \: cannot \: be \: found \\ Equation \: is \: in \: form \: a \frac{}{1} x + b \frac{}{1} y + c \frac{}{1}= 0\:and \\ a \frac{}{2} x + b \frac{}{2} y + c \frac{}{2} = 0 \\ where, \: \: \frac{a \frac{}{1} }{a \frac{}{2} } = \frac{b \frac{}{1} }{b \frac{}{2} } \\ Therefore \: lines \: are \: parallel \: to \: each \: other \\ Lines \: have \: no \: solution.\)

The composite mapping (f o g)(x) ≥ 3 for the functions f(x) = 2x + 1 and g(x) = x² + 1. And (f o g)(x) > 0 for the functions f(x) = x² and g(x) = x.

A mapping is composite when the co- domain of the first mapping is the domain of the second mapping.

For the functions f(x) = 2x + 1 and g(x) = x² + 1

If x > 0, say x = 1 then;

g(x) = 1² + 1

g(x) = 2

(f o g)(x) = 2(2) + 1

(f o g)(x) = 4 + 1

(f o g)(x) = 5

If x = 0, then;

g(x) = 0² + 1

g(x) = 1

(f o g)(x) = 2(1) + 1

(f o g)(x) = 2 + 1

(f o g)(x) = 3

For the functions f(x) = x² and g(x) = x

If x < 0, say x = -0.5, then;

g(x) = -0.5

(f o g)(x) = (-0.5)²

(f o g)(x) = 0.25

In conclusion, the composite mapping (f o g)(x) ≥ 3 for functions f(x) = 2x + 1 and g(x) = x² + 1 and (f o g)(x) > 0 for the functions f(x) = x² and g(x) = x.

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Y = mx + b, where m denotes the slope and b the y-intercept, is how the equation of the line is expressed in the slope-intercept form. We can see that the y-intercept of the line in our equation, y = 7 x + 4, is 4.

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Answer:

f^ - 1 (x) = x/3 + 1/3​ is not the inverse function of f(x) = 3x + 1

Step-by-step explanation:

F(x) = 3x + 1

Inverse:

x = 3y + 1

3y = x - 1

y = x/3 - 1/3 or f^ - 1 (x) = x/3 - 1/3​

so

f^ - 1 (x) = x/3 + 1/3​ is not the inverse function of f(x) = 3x + 1

We have 98 % confidence that the true mean time a student sleeps per night is between 6.2928 hours and  7.1832 hours.

Mean = (8.6 + 8.3 + 7.6 + 6 + 7.1 + 5.6 + 5.1 + 6)/ 8 =  6.7875

Standard deviation = √Σ(x - mean)²/n

Σ(x - mean)² = (8.6 - 6.7875)^2 + (8.3 - 6.7875)^2 + (7.6 - 6.7875)^2 + (6 - 6.7875)^2 + (7.1 - 6.7875)^2 + (5.6 - 6.7875)^2 + (5.1 - 6.7875)^2 + (6 - 6.7875)^2

Standard deviation  : \(\sqrt{11.82875}/8\)

s = 0.42991

Confidence interval is written in the form,

(Sample mean - margin of error, sample mean + margin of error)

The sample mean, x is the point estimate for the population mean.

Margin of error = z × s/√n

Where

sample standard deviation

number of samples

From the information given, the population standard deviation is unknown and the sample size is small, hence, we would use the t distribution to find the z score

In order to use the t distribution, we would determine the degree of freedom, df for the sample.

df = n - 1 = 8 - 1 = 7

Since confidence level = 98% = 0.98, α = 1 - CL = 1 - 0.98 = 0.02

α/2 = 0.02/2 = 0.01

the area to the right of z0.01 is 0.01 and the area to the left of z0.01 is 1 - 0.01 = 0.99

Looking at the t distribution table,

z = 2.998

Margin of error = 2.998 × 0.42/√8

                        = 0.4452

The lower limit of this confidence interval is

6.738 - 0.4452 = 6.2928

The upper limit of this confidence interval is

6.738 + 0.4452 = 7.1832

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Answer:

-2

Step-by-step explanation:

Answer:

-2

Step-by-step explanation:

the y intercept is the point on the graph where the line crosses the x axis

1. The quadratic function for the Area in terms of x: A(x) = 24x.

2. The cross-sectional area is maximized when the depth of the gutter is 0.

3. The maximum cross-sectional area is square inches 0.

To determine the depth of the gutter that maximizes its cross-sectional area and allows the greatest amount of water to flow, we need to follow a step-by-step process.

1. Write a quadratic function for the area in terms of x:

The cross-sectional area of the gutter can be represented as a rectangle with a width of 24 inches and a depth of x. Therefore, the area, A(x), is given by A(x) = 24x.

2. The cross-sectional area is maximized when the depth of the gutter is:

To find the value of x that maximizes the area, we need to find the vertex of the quadratic function. The vertex of a quadratic function in form f(x) = ax² + bx + c is given by x = -b/(2a). In our case, a = 0 (since there is no x² term), b = 24, and c = 0. Thus, the depth of the gutter that maximizes the area is x = -24/(2 * 0) = 0.

3. The maximum cross-sectional area is square inches:

Substituting the value of x = 0 into the quadratic function A(x) = 24x, we get A(0) = 24 * 0 = 0. Therefore, the maximum cross-sectional area is 0 square inches.

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In 2021 a 30-second commercial during the Super Bowl cost $5.6 million and the CPI was approximately 271.4. Assuming that price changes are simply due to inflation, when the CPI was 33.4 the estimated cost of a 30-second commercial during the first Super Bowl in 1967 would be approximately $68,900.

To calculate the cost of the 30-second commercial during the first Super Bowl in 1967, we can use the concept of inflation and the Consumer Price Index (CPI).

The CPI measures the average price change of a basket of goods and services over time. By comparing the CPI values of two different years, we can estimate the relative increase in prices due to inflation.

Given data:

Cost of a 30-second commercial in 2021 = $5.6 million

CPI in 2021 = 271.4

CPI in 1967 = 33.4

To calculate the cost in 1967, we need to adjust the 2021 cost for inflation using the CPI ratio:

Cost in 1967 = (Cost in 2021) * (CPI in 1967 / CPI in 2021)

Cost in 1967 = ($5.6 million) * (33.4 / 271.4)

Cost in 1967 ≈ $0.689 million

To round the cost to the nearest hundred dollars, we can multiply the cost by 100 and round it to the nearest whole number:

Cost in 1967 ≈ $68,900

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Answer:

According to the table, there are **12** trees that are more than 8m tall but not more than 16m tall.

Source: (1) the table below shows the height of trees in a park. how many trees .... https://brainly.com/question/28952390 Accessed 16/03/2023.

Answer:

A. Normal

B. Between 40.08 minutes and 43.92 minutes.

C. About 95 percent of these confidence intervals will contain the true population mean number of minutes of concentration and about 5 percent will not contain the true population mean number of minutes of concentration.

Step-by-step explanation:

Central Limit Theorem

The Central Limit Theorem estabilishes that, for a normally distributed random variable X, with mean \(\mu\) and standard deviation \(\sigma\), the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean \(\mu\) and standard deviation \(s = \frac{\sigma}{\sqrt{n}}\).

For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.

For a proportion p in a sample of size n, the sampling distribution of the sample proportion will be approximately normal with mean \(\mu = p\) and standard deviation \(s = \sqrt{\frac{p(1-p)}{n}}\)

x% confidence interval:

A confidence interval is built from a sample, has bounds a and b, and has a confidence level of x%. It means that we are x% confident that the population mean is between a and b.

Question A:

By the Central Limit Theorem, a normal distribution.

Question B:

We have that to find our \(\alpha\) level, that is the subtraction of 1 by the confidence interval divided by 2. So:

\(\alpha = \frac{1 - 0.95}{2} = 0.025\)

Now, we have to find z in the Ztable as such z has a pvalue of \(1 - \alpha\).

That is z with a pvalue of \(1 - 0.025 = 0.975\), so Z = 1.96.

Now, find the margin of error M as such

\(M = z\frac{\sigma}{\sqrt{n}}\)

In which \(\sigma\) is the standard deviation of the population and n is the size of the sample.

\(M = 1.96\frac{12}{\sqrt{150}} = 1.92\)

The lower end of the interval is the sample mean subtracted by M. So it is 42 - 1.92 = 40.08 minutes

The upper end of the interval is the sample mean added to M. So it is 42 + 1.92 = 43.92 minutes

Between 40.08 minutes and 43.92 minutes.

Question C:

x% confidence interval -> x% will contain the true population mean, (100-x)% wont.

So, 95% confidence interval:

About 95 percent of these confidence intervals will contain the true population mean number of minutes of concentration and about 5 percent will not contain the true population mean number of minutes of concentration.

Answer:

-28 1/3

Step-by-step explanation:

-8 1/3= -25/3

3 2/5= 17/5

-25/3*17/5= -28 1/3

The solution to the equation sqrt 2-3x / sqrt 4x = 2 is x = -2/3.

To solve the equation, we must first clear the denominators and simplify the equation. We can do this by multiplying both sides by sqrt(4x) and then squaring both sides. This gives us:
sqrt 2-3x = 4sqrt x
2 - 6x + 9x² = 16x
9x² - 22x + 2 = 0
Using the quadratic formula, we can find that x = (-b ± sqrt(b² - 4ac)) / 2a. Plugging in a = 9, b = -22, and c = 2, we get:
x = (-(-22) ± sqrt((-22)² - 4(9)(2))) / 2(9)
x = (22 ± sqrt(352)) / 18
x = (22 ± 4sqrt22) / 18
Simplifying this expression, we get:
x = (11 ± 2sqrt22) / 9
Therefore, the solution to the equation is x = -2/3.
To solve the equation sqrt 2-3x / sqrt 4x = 2, we must clear the denominators and simplify the equation. This involves multiplying both sides by sqrt(4x) and then squaring both sides.

After simplifying, we end up with a quadratic equation. Using the quadratic formula, we can find that the solutions are x = (11 ± 2sqrt22) / 9.

However, we must check that these solutions do not result in a division by zero, as the original equation involves square roots. It turns out that the only valid solution is x = -2/3.

Therefore, this is the solution to the equation.

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The z-statistic test was conducted to determine the Deviation of RPM, ASM, and LF from the mean. The test indicates that RPM, ASM, and LF significantly deviate from the mean.

Report on the Analysis of American Airlines (Domestic) PerformanceThe quantitative analysis focused on three variables- load factors, revenue passenger miles, and available seat miles for American Airlines.

The Bureau of Transportation Statistics data for domestic flights from January 2006 to December 2012 was retrieved for the analysis. The quantitative analysis also focused on finding critical statistical values like mean, median, mode, standard deviation, variance, and minimum/maximum variables. The results of the data are summarized in Table 2. Revenue Passenger Miles (RPM) mean is 6,624,897, the median is 6,522,230, and mode is NONE. The minimum is 5,208,159 and the maximum is 8,277,155. The standard deviation is 720,158.571, and the variance is 518,628,367,282.42.

Load Factors (LF) mean is 82.934, the median is 83.355, and mode is 84.56. The minimum is 74.91, and the maximum is 89.94. The standard deviation is 3.972, and the variance is 15.762. The Available Seat Miles (ASM) mean is 7,984,735, the median is 7,753,372, and mode is NONE. The minimum is 6,734,620, and the maximum is 9,424,489. The standard deviation is 744,469.8849, and the variance is 554,235,409,510.06.Figure 1 above displays the performance of American Airlines (Domestic).

The mean RPM is 7,984,735, and the linear regression line is y = 50584x - 2.53E+8. The linear regression line indicates a positive relationship between RPM and year, with a coefficient of determination, R² = 0.6806. A coefficient of determination indicates the proportion of the variance in the dependent variable that is predictable from the independent variable. Therefore, 68.06% of the variance in RPM is predictable from the year. A one-way ANOVA analysis of variance test was conducted to determine the equality of means of three groups of variables; RPM, ASM, and LF. The null hypothesis is that the means of RPM, ASM, and LF are equal.

The alternative hypothesis is that the means of RPM, ASM, and LF are not equal. The level of significance is 0.05. The ANOVA results indicate that there is a significant difference in means of RPM, ASM, and LF (F = 17335.276, p < 0.05). Furthermore, a post-hoc Tukey's test was conducted to determine which variable means differ significantly. The test indicates that RPM, ASM, and LF means differ significantly.

The skewness test was conducted to determine the symmetry of the distribution of RPM, ASM, and LF. The test indicates that the distribution of RPM, ASM, and LF is not symmetrical (Skewness > 0).

Additionally, the z-statistic test was conducted to determine the deviation of RPM, ASM, and LF from the mean. The test indicates that RPM, ASM, and LF significantly deviate from the mean.

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Answer:

2/5

Step-by-step explanation:

4 raspberry / 10 total

4/10

2/5

Answer:

*add*

first lets take and example using 0.1 and 0.2

0.1

+0.2

=0.3

p/s : make sure the decimal points are alligned

*subtract*

we use the same rule as the above make sure the decimal point are alligned

0.2

-0.1

=0.1

*mutiply*

first vanish the decimal points

example 0.2 becomes 2.

if 0.9 becomes nine

then after you mutiply it, put the decimal point back where it should be

hope this helps! have a good day :)

The line which the shape is exactly equal two halves is called line of symmetry. For the given pentagon the line of symmetry is line which divide pentagon in two equal halves and vertices of each side halves lie at equal distance from the line of symmetry.

So if we divide the pentagon by line x = 3 then it passes through one its vertices and divide the pentagon in two halves which are equal and simillar to each other.

So for pentagon line of symmetry is x = 3.

Step-by-step explanation:

g(x) = f(x) that moved 4 units down and 1.5 units to the left.

the turning point in the middle of the function tells us this clearly.

to make that translation happen, it means

g(x) = f(x + 1.5) - 4 = (x - -1.5)³ + -4

the "-4" simply subtracts 4 units from every function result f(x) calculated. that moves everything down by 4 units.

and the "-1.5" (actually "x + 1.5") makes every function result of f(x) happen 1.5 units "earlier" for g(x). so, a shift to the left.

The standard error is of 0.2246, which means that the mean scores for samples of 30 vary around 0.2246 from the mean.

The confidence interval is the range of values that you expect your estimate to fall between a certain percentage of the time if you run your experiment again or re-sample the population in the same way.

The confidence interval formula is \(\bar x\pm t\frac{s}{\sqrt{n}}\).

Where, \(\bar x\) is the sample mean, t is the critical value, n is the sample size and s is the standard deviation for the sample.

Here,

\(\bar x\) =1.267, s=1.23, n=30

The standard error is Se= 1.23/√30

= 0.2246

Item a:

The standard error is of 0.2246, which means that the mean scores for samples of 30 vary around 0.2246 from the mean.

Item b:

Using a t-distribution calculator, considering a confidence level of 0.99 with 30 - 1 = 29 df, the critical value is t = 2.7564.

\(\bar x\pm tS_c\)

\(\bar x+ tS_c\) =1.267-2.7564(0.2246) =0.6479

\(\bar x- tS_c\) =1.267+2.7564(0.2246) =1.8861

Therefore, the 99% confidence interval to estimate the true mean score on this question is (0.6479, 1.8861). It means that we are 99% that the true mean score of all students in this question is between 0.6479 and 1.8861.

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If the spin lands on the space where the contestant wins nothing, then x = 0.

If the spin lands on a space where the contestant wins $1, then x = -1 + 1 = 0. If the spin lands on a space where the contestant wins $4, then x = -2 + 4 = 2.

The expected value of x can be calculated as follows:

E(x) = (333/555) × 0 + (111/555) × (-2 + 1) + (111/555) × (-2 + 4) = (111/555) * 2 = 0.4.

So, on average, the player's net gain per spin is 40 cents.

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Note that the coordinates of the point A' after rotating 90 degrees clockwise about the point (0,1) are (3, -4). (Option B)

To rotate a point 90 degrees  clockwise about a given point,we can follow these steps -

Translate the coordinates   of the given point so that the center of rotation is at the origin.   In this case,we subtract the coordinates   of the center (0,1) from the coordinates of point A (5,4) to get (-5, 3).

Perform the rotation by swapping the x and y coordinates and changing the sign of the   new x coordinate. In this case,we  swap the x and y coordinates of (-5, 3)   to  get (3, -5).

Translate the coordinates back to their original position   by adding the coordinates of the center (0,1)  to the result from step 2. In   this case, we add (0,1) to (3, -5) to get (3, -4).

Therefore, the coordinates   of the point A' after rotating 90 degrees clockwise about the point (0,1) are (3, -4).

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The statement that is true about the function is:

A function, in mathematics, an expression, rule, or law that defines a relationship between one variable (the independent variable) and another variable (the dependent variable).

Given:

The minimum value of the curve = (1.9, -5.7),

The maximum value = (0, 2)

The point the function crosses the x-axis (the x-intercept) = (-0.7, 0), (0.76, 0), and (2.5, 0)

The point the function crosses the y-axis (the y-intercept) = (0, 2)

The given points can be plotted using MS Excel, from which we have:

F(x) is less than 0 over the interval from x = -∞, to x = -0.7, and the interval from x = 0.76 to x = 2.5.

Hence, the correct option is A.

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Answer:

12/16 or 3/4

Step-by-step explanation:

Answer:

a

Step-by-step explanation:

The equation that can be used to determine the length of each equal piece is \(4x + 2\dfrac{1}{4} = 12\) and this can be determined by forming the linear equation.

Given :

The following steps can be used in order to determine the equation that can be used to determine the length of each equal piece:

Step 1 - The linear equation can be formed in order to determine the equation that can be used to determine the length of each equal piece.

Step 2 - Let the length of one piece be 'x'.

Step 3 - So, the linear equation that represents the total length of the board is:

\(4x + 2\dfrac{1}{4} = 12\)

Therefore, the correct option is C).

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1) The lower limit of the confidence Interval is: 1489.77.

The upper limit of the confidence Interval is: 1530.23

2) The lower limit of the confidence Interval is: 1478.32

The upper limit of the confidence Interval is: 15411.68

The formula to find the confidence interval is:

CI = x' ± z(σ/√n)

where:

CI is confidence interval

x' is sample mean

z is z-score at confidence level

σ is standard deviation

n is sample size

1) The parameters are:

σ = $234

x' = $1510

n = 362

z at 90% CL = 1.645

Thus:

CI = 1510 ± 1.645((234/√362)

CI = 1510 ± 20.23

CI = (1489.77, 1530.23)

2) The parameters are:

σ = $234

x' = $1510

n = 362

z at 99% CL = 2.576

Thus:

CI = 1510 ± 2.576((234/√362)

CI = 1510 ± 31.68

CI = (1478.32, 15411.68)

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Answer:

First coin Second coin outcome

H T HT

T H TH

T T TT

Step-by-step explanation:

First coin     Second coin             outcome

H               T                               HT

T               H                               TH

T               T                                TT

If the data is not skewed, then the mean is the best measure of center.

This then also includes the standard deviation because the standard deviation relies on the mean.

To get the mean, add up the data values:

5+6+7+7+7+8+8+9+9+9+9+9+10+10+11 = 124

Then divide by the sample size n = 15

124/n = 124/15 = 8.267 approximately

Once you determine the mean, you can then determine the standard deviation which involves a bit more complicated steps. The rough outline is:

Once again, step 1 shows how critical the mean is to finding the standard deviation. The standard deviation measures how far each value is from the mean on average. In other words, it's like a measure of the average distance from the mean.

Use of spreadsheet software is strongly recommended to keep track of everything. You can also use a standard calculator to compute the standard deviation. There are also tons of free online calculators that can help out with that as well.

-----------------------------------------------------------

If the data was skewed to one side, then the median is the better measure of center because it is not affected by outliers. The IQR (interquartile range) is used instead of the standard deviation for skewed distributions.

Answer:

3a(1+7b)=0 3a=0 a=0 1+7b= 0 b= - 1/7 factors are 0,-1/7.

The factors of the given expression 3a are 3 and a.

The factors are the polynomials which are multiplied to produce the original polynomial.

The given expression is 3a.

A factor is a number that can be multiplied by another number to equal a given product. For example, if we multiply 2 and 3 together, the product is 6, so 2 and 3 are factors of 6.

Here, 3a can be written as 3×a

Therefore, the factors of the given expression 3a are 3 and a.

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Therefore, the probability that a woman will give birth to two boys is only one in three, whereas the probability that a man will do so is one in two.

The area of mathematics known as probability deals with numerical representations of the likelihood that an event will occur or that a statement is true. An event's probability is a number between 0 and 1, where, roughly speaking, 0 denotes the event's impossibility and 1 denotes certainty.

Here,

The woman may have at least one boy in the three following ways: 1) older boy, younger girl; 2) older girl younger boy; 3) older boy, younger boy.

But the man's children may be distributed in only two ways: 1) older boy, younger girl; or 2) older boy, younger boy.

So the chances are only 1 out of 3 that the woman has two boys, but the chances are 1 out of 2 that the man has two boys.

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Answer:

513,000,000

Step-by-step explanation:

To write five hundred thirteen million in numbers change “five hundred thirteen million” to “513”, then multiply 513 by 106.

Alternatively, move the decimal point 6 places to the left:

513 × 106 = 513000000,

513 → 5,130 → 51,300 → 513,000 → 5,130,000 → 51,300,000 → 513,000,000.

Besides, five hundred thirteen million means:

513 × 10^6

513000000 as a whole number

513M in abbreviated form

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