Use distributive property

Question 1. 2f+10

Question 2. 20+24g

Question 3. 32b - 20


simplify the expression

Question 4. 24h + 3d - 10hn+ 8d

Question 5. 12s + 4 + 4s - 2

Answer:

Dan bought 44.65 liters of gas.

Step-by-step explanation:

The gas Dan bought on Friday and Saturday in gallons is

[tex]5\frac{1}{4}+6\frac{1}{2}[/tex]

[tex]=\frac{21}{4} +\frac{13}{2}[/tex]

We collect LCM for the denominators,

[tex]=\frac{21+26}{4}[/tex]

[tex]=\frac{47}{4}[/tex]gallons

We now convert to liters using the relation,

[tex]1\:gallon=3.8\: liters[/tex]

Let [tex]\frac{47}{4}\:gallons=x\:liters[/tex]

Then,

[tex]x=3.8\times \frac{47}{4}[/tex]

[tex]x=\frac{38}{10}\times \frac{47}{4}[/tex]

[tex]x=\frac{19}{5}\times \frac{47}{4}[/tex]

[tex]x=\frac{893}{20}=44.65[/tex]

Therefore Dan bought 44.65 liters of gas.

Assume the radius of the the earth is ~4000 miles.

radius of orbit = 4000 +200 = 4200 miles

In 4 hrs it orbits 2Pi*r =2pi*4200= 8400pi miles

In 1 hr it would travel (8400pi/4 )

= 2100pi = 6597.3445 miles (exact value)

= 6597 miles ( approximate)

The equation of line that is parallel to the line [tex]y-1=4\left({x+3}\right)[/tex]   and passes through the point [tex]\left({4,32}\right)[/tex]  is [tex]\boxed{{\mathbf{y=4x+16}}}[/tex]  and it matches with [tex]\boxed{{\mathbf{OPTION}}\,{\mathbf{D}}}[/tex] .

Further explanation:

It is given that the equation of line is [tex]y-1=4\left({x+3}\right)[/tex]  and passes through point [tex]\left({4,32}\right)[/tex] .

Rewrite the given equation [tex]y-1=4\left({x+3}\right)[/tex]  as follows:

[tex]\begin{aligned}y-1&=4\left({x+3}\right)\\y-1&=4x+12\\y&=4x+12+1\\y&=4x+13\\\end{aligned}[/tex]

Now, compare the obtained equation of line [tex]y=4x+13[/tex]  with the standard equation of line [tex]y=mx+b[/tex] .

[tex]\begin{aligned}m&=4\\b&=13\\\end{aligned}[/tex]

Therefore, the slope is [tex]4[/tex] .

It is given that both lines are parallel to each other so the product of slope must be equal.

[tex]{m_1}={m_2}[/tex]                                                          …… (1)

Substitute [tex]4[/tex]  for [tex]{m_1}[/tex]  in equation (1) to obtain the value of slope [tex]{m_2}[/tex] .

[tex]{m_2}=4[/tex]  

Therefore, the slope is [tex]4[/tex] .

It is given that the line passes through point [tex]\left({4,32}\right)[/tex] .

The point-slope form of the equation of a line with slope [tex]m[/tex]  passes through point [tex]\left({{x_1},{y_1}}\right)[/tex] is represented as follows:

[tex]y-{y_1}=m\left({x-{x_1}}\right)[/tex]                                       …… (2)

Substitute [tex]4[/tex]  for [tex]{x_1}[/tex] , [tex]32[/tex]  for [tex]{y_1}[/tex]  and [tex]4[/tex]  for [tex]m[/tex]  in equation (2) to obtain the equation of line.

[tex]\begin{aligned}y-32&=4\left({x-4}\right)\\y-32&=4x-16\\y&=4x-16+32\\y&=4x+16\\\end{aligned}[/tex]

Therefore, the equation of line is [tex]y=4x+16[/tex] .    

Now, the four options are given below.

[tex]\begin{gathered}{\text{OPTION A}}\to y=-x+33\hfill\\{\text{OPTION B}}\to y=-x+36\hfill\\{\text{OPTION C}}\to y=4x-16\hfill\\{\text{OPTION D}}\to y=4x+16\hfill\\\end{gathered}[/tex]

Since OPTION D matches the solution that is [tex]y=4x+16[/tex] .                                                                                                              

Thus, the equation of line that is parallel to the line [tex]y-1=4\left({x+3}\right)[/tex]  and passes through the point [tex]\left({4,32}\right)[/tex]  is [tex]\boxed{{\mathbf{y=4x+16}}}[/tex]  and it matches with [tex]\boxed{{\mathbf{OPTION}}\,{\mathbf{D}}}[/tex] .

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Answer Details:

Grade: Junior High School

Subject: Mathematics

Chapter: Coordinate Geometry

Keywords: Coordinate Geometry, linear equation, system of linear equations in two variables, variables, mathematics, equation of line, line, passes through point.

Answer:

We bought five 3 3/4 pound bags of bird seed.

A :

Total weight is = [tex]3\times(\frac{3}{4} )=\frac{9}{4}[/tex] pounds of bird seed.

In mixed fraction it is : [tex]2\frac{1}{4}[/tex] pounds

B :

As given, each smaller bag contains 1 1/2 pounds, so 9/4 pounds can make:

=[tex]\frac{\frac{9}{4}}{\frac{3}{2}}[/tex]= 18/12 = 3/2 bags

C :

We can make 1 full bag and will have left out enough for half of another bag. Half of a 3/2 pound is :

[tex]1/2(3/2)[/tex] = 3/4 of a pound.

Answer:

B. Is the Answer Because its the only one that is simplified.

Step-by-step explanation:

Have A Nice Day!

Answer: 2inches

Step-by-step explanation:

Answer:

Answer is C [tex]P = 2x + 3y[/tex]

Step-by-step explanation:

Selling price of candy bar X =$2

Selling price of candy bar Y =$3

So if Julie sells x from X candy bars and y bars from Y candy bars,

Profit made from selling X candy bars = [tex]2\times x[/tex]

Profit made from selling Y candy bars = [tex]3\times y[/tex]

Therefore, assuming that there is no cost for the candy bars the profit by selling candy bars can be represented by the following objective function:

[tex]P = 2x + 3y[/tex]

Therefore, answer is C

A contiguous subsequence of a list is a subsequence made up of consecutive elements.

A contiguous subsequence of a list s is a subsequence made up of consecutive elements of s. For example, if s is [1, 2, 3, 4, 5], a contiguous subsequence could be [2, 3, 4].

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The correct options is 3.  (3 - x + 2x - 4 + 2x) simplifies to (-1 + 3x ), which is equivalent.

The given expression is (6 + (-x) + 2x + (-7) + 2x). Simplifying this expression by combining like terms results in ( -1 + 3x). To check for equivalent expressions, we evaluate each option:

1. x + x + 6 - 7 + x simplifies to (3x - 1), which is not equivalent.

2. (2x + 2 + x) simplifies to (3x + 2), which is not equivalent.

3. (3 - x + 2x - 4 + 2x) simplifies to (-1 + 3x ), which is equivalent.

4. (x - 1) is not equivalent.

5. (x + 1) is not equivalent.

Therefore, only the expression (3 - x + 2x - 4 + 2x) is equivalent to the given expression. The simplified form of the original expression is ( -1 + 3x), and the equivalent expression confirms this result by matching the simplified terms.

Complete question:

Which expressions are equivalent to 6 +(–x) + 2x + (–7) + 2x? Check all that apply.

The expressions that are equivalent to [tex]\(6 + x + 2x - 7 + 2x\)[/tex] are:

a. [tex]\(x + x + 6 - 7 + x\)[/tex]

c.[tex]\(3 - x + 2x - 4 + 2x\)[/tex]

The correct option is (a)&(c).

To find which expressions are equivalent to [tex]\(6 + x + 2x - 7 + 2x\)[/tex], let's simplify the given expression first:

[tex]\[6 + x + 2x - 7 + 2x\][/tex]

Combining like terms:

[tex]\[6 - 7 + x + 2x + 2x\][/tex]

[tex]\[(-1) + 5x\][/tex]

Now, let's check each option to see which ones are equivalent:

a.[tex]\(x + x + 6 - 7 + x\)[/tex]

Combine like terms:

[tex]\(3x - 1\)[/tex]

This expression is equivalent.

b. [tex]\(2x + 2 + x\)[/tex]

Combine like terms:

[tex]\(3x + 2\)[/tex]

This expression is not equivalent.

c. [tex]\(3 - x + 2x - 4 + 2x\)[/tex]

Combine like terms:

[tex]\(3 + 5x - 4\)[/tex]

[tex]\(5x - 1\)[/tex]

This expression is equivalent.

d. [tex]\(x - 1\)[/tex]

This expression is not equivalent.

e. [tex]\(x + 1\)[/tex]

This expression is not equivalent.

So, the expressions that are equivalent to [tex]\(6 + x + 2x - 7 + 2x\)[/tex] are:

a. [tex]\(x + x + 6 - 7 + x\)[/tex]

c.[tex]\(3 - x + 2x - 4 + 2x\)[/tex]

complete question given below:

Which expressions are equivalent to 6 +(x)+2x+(- 7) + 2x? Check all that apply.

a.x+x+6-7+x

b.2x+2+x

c.3-x+2x-4+2x

d.x-1

e.x+1.

a. First we solve the finite population correction factor σx from the formula:

σx = [s / sqrt(n)] * sqrt [(N – n) / (N – 1)]

σx = [0.40 / sqrt(16)] * sqrt[(500 – 16) / (500 – 1)]

σx = 0.0985

Then we compute for z score when x ≥ 3 minutes:

z = (x – m) / σx

z = (3 – 3.10) / 0.0985

z = -1.015

From the tables, the probability (p value) using right tailed test is:

P = 0.845 = 84.5%

b. At P = 0.85, the z score is z = 1.04

1.04 = (x – 3.10) / 0.0985

x = 3.20

Hence there is a 85% chance it will be below 3.20 minutes

Final answer:

The probability that the average time spent per customer will be at least 3 minutes is approximately 0.8413. There is an 85% chance that the sample mean will be below approximately 3.359 minutes.

Explanation:

a. To find the probability that the average time spent per customer will be at least 3 minutes, we need to find the probability that the sample mean is greater than or equal to 3 minutes. Since the population standard deviation is known and the sample size is large (n=16), we can use the z-score formula and the standard normal distribution to calculate the probability. The z-score is calculated as follows:

z = (x - µ) / (σ / √n)

where x is the sample mean, µ is the population mean, σ is the population standard deviation, and n is the sample size. Substituting the values into the formula:

z = (3 - 3.10) / (0.40 / √16) = -0.1 / (0.40 / 4) = -0.1 / 0.1 = -1

Looking up the corresponding area to the left of z=-1 in the standard normal distribution table, we find that the probability is approximately 0.1587. Therefore, the probability that the average time spent per customer will be at least 3 minutes is approximately 0.8413.

b. To find the value below which there is an 85% chance that the sample mean will be, we need to find the z-score that corresponds to the cumulative probability of 0.85. Using the standard normal distribution table, we find that the z-score is approximately 1.036. Substituting the values into the z-score formula:

1.036 = (x - 3.10) / (0.40 / √16)

Solving for x:

1.036 * (0.40 / √16) + 3.10 = x

x ≈ 0.259 + 3.10 ≈ 3.359

Therefore, there is an 85% chance that the sample mean will be below approximately 3.359 minutes.

Answer:

The property which is illustrated by the statement 5g+7= 7 + 5g is:

Commutative property

Step-by-step explanation:

Commutative property states that:

If a and b are two elements defined under the operation *

Then, a*b=b*a

Here, we are given

5g+7= 7 + 5g

i.e. a=5g, b=7 and * = +

Hence, the property which is illustrated by the statement 5g+7= 7 + 5g is:

Commutative property

 Construct a 95% confidence interval estimate of the mean net change in LDL cholesterol after the garlic treatment. What does the confidence interval suggest about the effectiveness of garlic in reducing LDL​cholesterol?

sample mean = x-bar = 4.7
ME = 1.96*15.6/sqrt(43) = 4.663

95% CI: 4.7 - 4.663 < u < 4.7 + 4.663

The 95% confidence interval of (4.5, 9.5) suggests that the true average change in LDL cholesterol after the garlic treatment is likely to fall within this range. However, with a p-value of 0.1494, there isn't enough statistical evidence to conclusively affirm that the garlic treatment significantly reduces LDL cholesterol levels.

To construct a 95% confidence interval estimate of the mean net change in LDL cholesterol after the garlic treatment, you have to be given or calculate the sample mean, the standard error, and the degrees of freedom. These factors depend on the data provided.

In this scenario, using the pre-calculated confidence interval provided, we have it at (4.5, 9.5). This means that we are 95% confident that the true population mean net LDL cholesterol change after garlic treatment is somewhere between a 4.5 unit decrease and a 9.5 unit decrease.

The effectiveness of the garlic treatment cannot be determined solely by this confidence interval, but this range might suggest a possible decrease in LDL cholesterol levels.

However, keep in mind that the p-value signifies the strength of the evidence against the null hypothesis. A p-value of 0.1494, as stated in the problem, means there isn't enough evidence to significantly conclude that the garlic treatment reduced LDL cholesterol at the 5% significance level.

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Answer:

x = [tex]\frac{2}{3}\times t[/tex]

Step-by-step explanation:

We know the formula to represent the speed is,

Speed = [tex]\frac{\text{Distance}}{\text{Time}}[/tex]

If a car travels the distance = [tex]\frac{7}{3}[/tex] miles in [tex]\frac{7}{2}[/tex] minutes then the speed will be

Speed = [tex]\frac{\frac{7}{3}}{\frac{7}{2}}[/tex]

           = [tex]\frac{7}{3}\times \frac{2}{7}[/tex]

           = [tex]\frac{2}{3}[/tex] miles per minute

If the car travels x miles in t minutes then the equation to calculate the distance will be

[tex]\frac{2}{3}=\frac{x}{t}[/tex]

x = [tex]\frac{2}{3}\times t[/tex]

Therefore, the equation that represents the distance in terms of time will be

x = [tex]\frac{2}{3}\times t[/tex]

Final answer:

The normal distribution in question behaves according to the Empirical Rule, which states that about 68% of the data falls within one standard deviation of the mean in a bell-shaped, symmetric distribution. This percentage changes to about 95% within two standard deviations and over 99% within three standard deviations.

Explanation:

A normal distribution in which approximately 68% of the data values fall within one standard deviation of the mean behaves according to the Empirical Rule. This is a key concept of descriptive statistics that applies specifically to bell-shaped, symmetric distributions. According to the rule, about 68 percent of the data lies within one standard deviation of the mean, about 95 percent lies within two standard deviations, and over 99 percent lies within three standard deviations.

For example, if a distribution has a mean (μ) of 50 and a standard deviation (σ) of 6, then approximately 68 percent of the values (x) would lie between 44 (50 - 6) and 56 (50 + 6). These points are one standard deviation away from the mean and correspond to the z-scores of -1 and +1, respectively. It is important to remember that this rule only applies when the distribution is perfectly bell-shaped and symmetric.