how do you simplify decimals??

ex) simplify.
7.21 + 4.2

Answer:

The 95% confidence interval for the population's mean length of vacation, in days, is (4.24, 4.76).

The 92% confidence interval for the population's mean length of vacation, in days, is (4.27, 4.73).

Step-by-step explanation:

We have the standard deviations for the sample, which means that the t-distribution is used to solve this question.

The first step to solve this problem is finding how many degrees of freedom, we have. This is the sample size subtracted by 1. So

df = 85 - 1 = 84

95% confidence interval

Now, we have to find a value of T, which is found looking at the t table, with 84 degrees of freedom(y-axis) and a confidence level of \(1 - \frac{1 - 0.95}{2} = 0.975\). So we have T = 1.989.

The margin of error is:

\(M = T\frac{s}{\sqrt{n}} = 1.989\frac{1.2}{\sqrt{85}} = 0.26\)

In which s is the standard deviation of the sample and n is the size of the sample.

The lower end of the interval is the sample mean subtracted by M. So it is 4.5 - 0.26 = 4.24 days

The upper end of the interval is the sample mean added to M. So it is 4.5 + 0.26 = 4.76 days

The 95% confidence interval for the population's mean length of vacation, in days, is (4.24, 4.76).

92% confidence interval:

Following the sample logic, the critical value is 1.772. So

\(M = T\frac{s}{\sqrt{n}} = 1.772\frac{1.2}{\sqrt{85}} = 0.23\)

The lower end of the interval is the sample mean subtracted by M. So it is 4.5 - 0.23 = 4.27 days

The upper end of the interval is the sample mean added to M. So it is 4.5 + 0.23 = 4.73 days

The 92% confidence interval for the population's mean length of vacation, in days, is (4.27, 4.73).

Answer:

here you go! y = 2 x + 4. Swap sides so that all variable terms are on the left hand side. Swap sides so that all variable terms are on the left hand side. 2x+4=y. 2 x + 4 = y. Subtract 4 from both sides. Subtract 4 from both sides. 2x=y-4. 2 x = y − 4

Answer:

2, 4, -2

Step-by-step explanation:

The slope is directly in the equation, the variable m in the slope-intercept form of y = mx + b. This means that the slope is 2.

The y-intercept is the variable b in standard form, so 4 in this case.

To find the x-intercept, set y equal to zero.

0 = 2x + 4

2x = -4

x = -2

The cost to ship 1,800 lbs of goods from Atlanta to Louisville using overnight shipping is $7,200.

To calculate the cost of shipping 1,800 lbs of goods from Atlanta to Louisville using overnight shipping, we need to determine the price per 100 lbs and apply the 100% premium for overnight shipping.

From the information, we can see that the price per 100 lbs for the distance range of 401-600 miles is $200.

Since the distance from Atlanta to Louisville is 390 miles, which falls within the 401-600 miles range, we can use the corresponding price per 100 lbs of $200.

To calculate the cost, we need to divide the total weight of 1,800 lbs by 100 to get the number of 100 lb units: 1,800 lbs / 100 = 18 units.

Then, we multiply the number of units by the price per 100 lbs, taking into account the 100% premium for overnight shipping:

18 units * $200 * 2 = $7,200.

Therefore, the cost is $7,200.

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Answer:

x=7

y=4

Step-by-step explanation:

Answer:

Isosceles and scalene triangles can both be obtuse.

Shirts = 10$ Pants = 10$

Step-by-step explanation:

50 / 5 = 10$

3/1 = 10$

In this system of simultaneous equations, the cost of each shirt (x) equals $5 and the cost of each pair of pants (y) is $25.

This is a system of simultaneous equation problems in Mathematics. Let's denote the cost of one shirt as x and one pair of pants as y. Based on the problem information, you have these two equations:

1) 2x + 3y = 50

2) 3x + y = 40

To solve for x, you can multiply the second equation by three and subtract the first equation from it:

3*(3x + y) - (2x + 3y) = 50

After simplifying, you find that x (cost of each shirt) equals 5.

In order to find y (cost of each pair of pants), you can now substitute x = 5 into the second original equation: 3*5 + y = 40, which gives you y = $25, the cost of each pair of pants.

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Answer:Can somebody also help me with this. i'm confused please hurry!

Step-by-step explanation:

Answer:

a)9. b) 12

Step-by-step explanation:

a) | -6 -3 | .

-6-3 = -9

|-9| =9

b) | 0 - 12 |.

0-12=-12

|-12|=12

Answer:

x = all real numbers

Step-by-step explanation:

first you need to solve the first equation to figure out what y is.

4x - y = 2

add y to both sides of the equation

4x = 2 + y

subtract 2 from both sides of the equation

4x - 2 = y

now that you know what y is, you can substitute it in the next equation.

3y = 12x - 6

3(4x - 2) = 12x - 6

open the parenthesis

12x - 6 = 12x - 6

subtract 12x from both sides of the equation

-6 = -6

regardless of what x is, -6 will always equal -6.

so, the answer is all real numbers.

The value of the Test statistic =z=-1.67

We have the value of sigma = 6, n = 260

In a hypothesis test, a test statistic—a random variable—is computed from sample data. To decide whether to reject the null hypothesis, you can utilize test statistics. Your results are compared to what would be anticipated under the null hypothesis by the test statistic. The p-value is computed using the test statistic.

Now using the formula of Test static

Test statistic will be:  \(\mathrm{z}=\frac{\overline{\mathrm{x}}-\mu}{\frac{\sigma}{\sqrt{\mathrm{n}}}}\\\)

Where, n = total number of sample = 100

\(\bar x\) = mean of the given data

\(\mu\) = total number of hours taken to receive a basic driving licence.

So, putting the value given in the question,

We will get the value of test static as:

\(=\frac{99-100}{\frac{6}{\sqrt{260}}}=-1.67\)

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Given g(x) and h(x) below:

To find the quotient (g/h)(x), divide g(x) by h(x):

The first 5 terms of the sequence is given by A = { -4.8 , 1.92 , -0.768 , 0.3072 , -0.12288 }

Given data ,

Let the geometric sequence be represented as A

Now , the value of A is

A = 12 ( -2/5 )ⁿ

On simplifying , we get

when n = 1

A₁ = 12 ( -2/5 ) = -4.8

A₂ = 12 ( -2/5 )²

A₂ = 12 ( 4/25 ) = 1.92

A₃ = 12 ( -2/5 )³

A₃ = -12 ( 8/125 ) = -0.768

A₄ = 12 ( -2/5 )⁴

A₄ = 12 ( 16 / 625 ) = 0.3072

A₅ = 12 ( -2/5 )⁵

A₅ = -12 ( 32 / 3,125 ) = -0.12288

Hence , the geometric sequence is solved

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Scale factor back to original size = 1/7

        7x and 7 years.

This means the original size will be;

Length = 7x × 1/7

Width = 7y × 1/7

Hence, the scale factor will be 1/7 back to the original size.

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Answer:what percent of the yearly sales were for July and September. if the graph shows 123,000​

Step-by-step explanation:

The unit rate of computers per day using the graph is that 12 computers are made per day.

The unit rate is how many units of quantity correspond to the single unit of another quantity. We say that when the denominator in rate is 1, it is called unit rate. Unit rates is said to be the amount of something in each unit or per unit.

To obtain the unit rate of computers sold per day using the graph, we need to obtain the slope of the graph, which is the change in y per change in x

So, it is given by:

\(\text{Slope} = \dfrac{\text{change in y}}{\text{change in x}}\)

\(\text{Slope} = \dfrac{\text{y}_2-\text{y}_1}{\text{x}_2-\text{x}_1}\)

\(\text{y}_2 = 60 , \ \text{y}_1 = 36 , \ \text{x}_2 = 5, \ \text{x}_1 = 3.\)

\(\text{Slope} = \dfrac{(60 - 36)}{(5 - 3)} = \dfrac{24}{2} = 12\)

\(\bold{Slope = 12}\)

Unit rate = 12 computers per day.

The attachment of the graph is given below.

Therefore, the unit rate of computers per day is 12.

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Answer:

y = -2

Step-by-step explanation:

Y × 9 = -18

Y = -18 / 9

Y = -2

Therefore, using the multiplier formula, a $525,000,000 increase in RGDP would result in a total increase in spending of $2,625,000,000.

To use the multiplier formula, we need to know the marginal propensity to consume (MPC), which is the fraction of each additional dollar of income that is spent on consumption.

The multiplier formula is: Multiplier = 1 / (1 - MPC)

If we assume an MPC of 0.8 (meaning that for every additional dollar of income, 80 cents are spent on consumption), the multiplier would be:

Multiplier = 1 / (1 - 0.8) = 5

So, if the change in Real Gross Domestic Product (RGDP) is $525,000,000, the total increase in spending (including consumption, investment, government spending, and net exports) would be:

Total spending increase = Multiplier x RGDP change

Total spending increase = 5 x $525,000,000

Total spending increase = $2,625,000,000

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Answer:

\(PR = 37\)

Step-by-step explanation:

Given

\(PQ = 25\)

\(PQ = 2x +1\)

\(QR = x\)

Required

PQ

Since Q is between the given points, then:

\(PR = PQ + QR\)

This gives:

\(PR = 2x + 1 + x\)

Collect like terms

\(PR = 2x + x+ 1\)

\(PR = 3x + 1\)

Next, solve for x

We have:

\(PQ = 25\)

\(PQ = 2x +1\)

This gives:

\(2x + 1 = 25\)

Collect like terms

\(2x = 25 -1\)

\(2x = 24\)

Divide by 2

\(x = 12\)

So:

\(PR = 3x + 1\)

\(PR = 3 * 12 + 1\)

\(PR = 37\)

With a mean of $32,500 and a standard deviation of $2,500. The z-score for a sales associate who earns $37,500 is 2.

The z-score, also known as a standard score, is a measure of how many standard deviations a given value is from the mean. It is used to standardize the data and make it easier to compare and interpret. The formula for the z-score is:

z = (x - μ) / σ

where x is the value of interest, μ is the mean, and σ is the standard deviation.

In this case, the mean annual salary for sales associates from a particular store is $32,500 and the standard deviation is $2,500. We want to find the z-score for a sales associate who earns $37,500. Plugging in the values, we get:

z = ($37,500 - $32,500) / $2,500 = 2

This means that the sales associate's salary is 2 standard deviations above the mean.

Interpreting the z-score can help us understand how unusual or typical a given value is in comparison to the mean. In this case, a z-score of 2 indicates that the sales associate's salary is relatively high compared to the mean, but it is not an extremely high salary.

We can use a standard normal table to find the proportion of the data that falls below a given z-score, or to find the corresponding value for a given proportion of the data.

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Answer:

1/8 is the bigger fraction

Step-by-step explanation:

When comparing fractions with different denominators, and the numerator is one, like 1/8. The one with the smaller number for the denominator is greater.

You could also compare them by finding common denominators, so for 1/8 and 1/9, a common denominator would be /63. So you would take \(\frac{1}{8}\) and multiply that by \(\frac{9}{9}\). You would then get \(\frac{9}{63}\). When you take \(\frac{1}{9}\) times \(\frac{8}{8}\) you get \(\frac{8}{63}\). So when comparing you can see that 1/8 is greater than 1/9.

The state income tax owed on a $40,000 per year salary is $1,500.

We have,

To calculate the state income tax owed on a $40,000 per year salary, we need to use the progressive tax rate table given in the problem.

Since $40,000 falls within the income range of $10,001 to $50,000, the tax rate that applies is 5%.

The amount of income that falls within this range.

= $40,000 - $10,000

= $30,000.

So we can calculate the tax owed on this income as:

tax = 5% x $30,000

= 5/100 x 30,000

= $1,500

Therefore,

The state income tax owed on a $40,000 per year salary is $1,500.

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Answer: 1,800

Step-by-step explanation:

The graph of the linear inequality y ≥ 2x - 5 is attached below with it's shaded part included.

The graph of an inequality in two variables is the set of points that represents all solutions to the inequality. A linear inequality divides the coordinate plane into two halves by a boundary line where one half represents the solutions of the inequality.

In the given problem, the inequality presented is;

y ≥ 2x - 5

To graph this, we would use a graphing calculator to find the boundary lines and plane.

In the graph below, the x and y intercept is at (2.5, -5) and the shaded part is on the left side of the graph.

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Answer:

2/5

Step-by-step explanation:

4 raspberry / 10 total

4/10

2/5

Answer: -2

Step-by-step explanation:

We can combine the fundamentals of mental math and the brain to calculate the problem when x is -2. You wake up noticing x is -2 and you instantly know the answer and solved in less than a second.