Directions: Solve each of the following equations.

1. 3x - 12 = 6


2. 2x + 4= 8

3. 12s - 12=12

4. 14s + 7 = 35

5. 3s - 12 = 6

6. 18t + 9 = 34

7. 21x + 7 = 28

8. 50y + 3 = 103

9. 1/4x - 6 = 18

10. 26x + 2 = 18

11. 6 - 2x = 18

12. 14 + s = 21

13. 16x - 4 = 28

14. 19x - 1 + 3 = 40

15. 100t = 194

16. 500x + 100 = 1100

17. 60-3x + 3 = 114

Step-by-step:

1)Combine multiplied terms into a single fraction

1/7a+ 1/7

1a/7+1/7

2)Multiply by 1

3)Combine fractions with a common denominator

Solution

a+1/7

Hope That helps!

These two lines intercept on a graph on the coordinate X(0, 1) Y(9, 7).

The term "intercept" refers to the location where a line or curve intersects an axis on a graph. An object's x-intercept is defined as where a point crosses the x-axis. The term "y-intercept" refers to a point that crosses the y-axis. The intersection of the x-axis and the y-axis is what is meant by a line's intercept.

step1

y=-2x+9

graph the line using the slope and y intercept or two points

y=-2x+9

X(0,1) Y(9,7)

step2

y=3x-6

slope 3 y intercept (0,-6)

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Answer:

Step-by-step explanation:

Answer:

42

Step-by-step explanation:

trust me i had the same answer and it was right

Answer:

the answer is -6,5

Step-by-step explanation:

just look at the left side ( the x axis )first then right(the y axis)

The purpose of Lend-Lease was to provide military aid to countries fighting against the Axis powers during set  World War II.

The purpose of Lend-Lease was to provide military aid to countries fighting against the Axis powers during World War II. The program was enacted by the United States in 1941 and allowed the US to provide war materials to its allies without requiring repayment. It was a major factor in the Allied victory, as it allowed the US to supply its allies with much needed war material and resources. The US provided a variety of goods, including food, oil, weapons, and tanks. It also supplied the Soviet Union with millions of tons of military equipment and supplies. Lend-Lease was instrumental in helping the Allies win the war, as it allowed them to gain a huge advantage over the Axis powers by providing essential supplies and resources.

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The worth of the comic in 15 years is $784.41.

If the value of the comic is increasing it means it is appreciating in value. As a result of the appreciation, the price of the comic increases with the passage of time.

FV = P (1 + r)^n

$360 x (1.05)^15 = $784.41

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Answer:

The final answer is 748.41

Step-by-step explanation:

a) The sampling distribution of the sample mean has mean μ=300 and standard deviation  is 4.

b)Normal distribution.

c)No. Because the distribution of the variable under consideration is not specified, a sample size of at least 30 is needed for part (a) to be true.The correct answer is B.

a. The sampling distribution of the sample mean for samples of size 49 is approximately normally distributed with a mean (μ) of 300 and a standard deviation (σ) of 28/√49 (which is 28/7 or 4).

b. For part (a) to be true, the assumption made about the distribution of the variable under consideration is C. Normal distribution.

c. The statement in part (a) is still true if the sample size is 16 instead of 49 because of the Central Limit Theorem. However, the standard deviation will change.

The correct answer is B. No. Because the distribution of the variable under consideration is not specified, a sample size of at least 30 is needed for part (a) to be true.

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The correct choice is B which states the geometric series or state k Σ * 18 k=0 diverges.

To evaluate the series Σ(18^k) from k = 0, we use the formula for the sum of a geometric series:

S = a * (1 - r^n) / (1 - r)

where 'n' is the number of terms.

The given series is a geometric series with first term 'a' = 1 and common ratio 'r' = 18.  

In this case, a = 18^0 = 1 (the first term), r = 18 (the common ratio), and we need to find the sum S.

Plugging these values into the formula, we have:

S = 1 * (1 - 18^n) / (1 - 18)

Since the common ratio 'r' is greater than 1, the series diverges.

A geometric series converges if the absolute value of the common ratio (r) is less than 1. In this case, the absolute value of 18 is greater than 1 (|18| > 1), so the series diverges.

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The linear equation doesn't have a solution.

The linear equation given is illustrated as: 4x-(2x-1) = x+5+x-6

This will be solved thus:

4x - 2x + 1 = x+5+x-6

4x - 2x + 1 = 2x - 1.

2x + 1 = 2x - 1

Collect like terms

2x - 2x = -1 - 1

0 = -2

This illustrates that the equation doesn't have a solution.

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\(5x-6-x=2x+2\\\\5x-x-2x=2+6\\\\2x=8 \ \ /:2\\\\x=4\\\\\huge\boxed{\text{There is one solution at x=4}}\)

Answer:

There is one solution at x+4

Step-by-step explanation:

(a) This is an observational study.

The reason is that the researchers did not manipulate any variables or conditions; they simply observed and collected data on the two groups of babies (VLBW and normal birth weight) as they grew up.
(b) The p-value (0.0013) is less than the significance level (typically 0.05), we reject the null hypothesis.  

There is sufficient evidence to suggest that the graduation rate among the VLBW group is significantly lower than the normal-birth-weight controls.

To determine if the graduation rate among the VLBW group is significantly lower than the normal-birth-weight controls, we can perform a hypothesis test using the proportion of high school graduates in each group.
State the null and alternative hypotheses.
Null hypothesis (H0):

There is no significant difference in graduation rates between the VLBW group and the control group (\(p_VLBW = p_control).\)
Alternative hypothesis (Ha):

The graduation rate among the VLBW group is significantly lower than the control group \((p_VLBW < p_control).\).

Calculate the sample proportions and the pooled proportion.
\(p_VLBW\) = 179/242 = 0.7397
\(p_control = 193/233 = 0.8283.\)
\(p_pooled = (179 + 193) / (242 + 233) = 0.7842\)
Calculate the test statistic.
\(z = (p_VLBW - p_control) / sqrt(p_pooled * (1 - p_pooled) * (1/242 + 1/233)) = -3.0074\)
Determine the p-value.
Using a z-table or calculator, the p-value for z = -3.0074 is approximately 0.0013.

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Answer:

\(a^6\)

Step-by-step explanation:

a^3 * a^3

= a^3+3

= a^6

Answer:

a⁶ is the simplified expression of a³ • a³

Using the linear rate data provided and using simple unitary method, The answer is $150.

A straight-line link between two variables is referred to statistically as a linear relationship (or linear association).

In mathematics, data is a collection of facts and figures that can take any shape, whether it be numerical or not. You can calculate numerical data, which is always gathered in number form and includes things like student test results, employee salaries, football team member heights, etc.

Total balance after 6 months = $750

Rate = $100 per month

Time = 6 months

Balance deposited at the rate in 6 months = 100 * 6

=$600

Initial Balance = $750 -  $600

=$150

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Answer:

7

Step-by-step explanation:

Let's simplify step-by-step.

−2c+7+2c

Combine Like Terms:

=−2c+7+2c

=(−2c+2c)+(7)

=7

The conjugate base of the weak acid hc2h3o2 (acetic acid) can be determined by removing a proton (H+) from the acid molecule. The formula for the conjugate base is C2H3O2- (acetate ion).

The formula for acetic acid (hc2h3o2) suggests that it consists of the elements hydrogen (H), carbon (C), and oxygen (O). To determine the formula of its conjugate base, we remove a proton (H+) from the acid molecule. Removing a proton results in the formation of an anion, which has a negative charge to maintain overall charge neutrality.

The removal of a proton from hc2h3o2 leads to the formation of the acetate ion, which has a formula of C2H3O2-. The C2H3O2- ion is referred to as the conjugate base of acetic acid.

In summary, the formula for the conjugate base of the weak acid hc2h3o2 (acetic acid) is C2H3O2- (acetate ion).

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Answer:

See below

Step-by-step explanation:

20% loss a year with initial value of £6000 can be shown as function:

V(t) - is the value after t years

a) t = 1 year

b) t = 3 years

c) t = 8 years

Given that 1 kilometer = 0.62 mile, 36 inches = 1 yard, and 1 mile = 1760 yards, 1 km has approximately 39,283.2 inches.

In mathematics, conversion is the process of changing the value of one form or unit to another. It can be changing ones unit of length, weight, volume or even currency to another.

A conversion factor is a number used to change one set of units to another, either by multiplying or dividing.

From the problem, the conversion factors are given as

1 kilometer = 0.62 mile

36 inches = 1 yard

1 mile = 1760 yards

To convert 1 kilometer into inches, first, convert 1 kilometer to miles using the conversion factor, 1 kilometer = 0.62 mile

1 km = 0.62 miles

Then, convert miles to yards using the conversion factor, 1 mile = 1760 yards

1 km = 0.62 miles = 0.62 (1760 yards)

1 km = 0.62 miles = 1091.2 yards

Lastly, convert yards to inches using the conversion factor, 36 inches = 1 yard

1 km = 0.62 miles = 1091.2 yards = 1091.2 (36 inches)

1 km = 0.62 miles = 1091.2 yards = 39,283.2 inches

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The hydroxide-ion concentration or pOH of HNO₃ solution comes to be 8.02.

The pOH of a solution is the negative logarithm of the hydroxide-ion concentration.

or pOH = -log[OH⁻]

The hydroxide-ion concentration OH⁻ of HNO₃ solution = 9.5 * 10⁻⁹ million.

So, the pOH of the HNO₃ solution =-log[9.5* 10⁻⁹] = 8.02

Therefore, the hydroxide-ion concentration or pOH of HNO₃ solution comes to be 8.02.

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Answer:

8.02

Step-by-step explanation:

trust

Answer:

Adjacent = 9.75 inches.

Step-by-step explanation:

Given the following data;

Hypothenus = 12 inches

Opposite = 7 inches

To find the other leg i.e adjacent, we would use Pythagorean' theorem given by the formula;

Hypothenus² = opposite² + adjacent²

Substituting into the formula, we have;

12² = 7² + adjacent²

144 = 49 + adjacent²

Adjacent² = 144 - 49

Adjacent² = 95

Taking the square root of both sides, we have;

Adjacent = 9.75 inches.

Therefore, the other leg is 9.75 inches.

Answer:

9k + 8

General Formulas and Concepts:

Algebra I

Step-by-step explanation:

Step 1: Define expression

-6k + 15k + 8

Step 2: Simplify

And we have our final answer!

The maximum volume of the prism is 1728 cubic centimeters.

To find the dimensions of the prism with maximum volume, we need to consider the relationship between the volume of the prism and its dimensions.

Let's assume the base of the right triangular prism is an isosceles right triangle with legs of length 'a'. The height of the prism will be 'h'. The prism is inscribed in a hemisphere with a radius of 12 cm.

First, let's determine the relationship between 'a' and 'h'. Since the base of the prism is on the great circle of the hemisphere, the hypotenuse of the triangular base is equal to the diameter of the hemisphere, which is twice the radius. Therefore, the hypotenuse of the base is 2 * 12 = 24 cm.

By using the Pythagorean theorem, we can find 'a':

a^2 + a^2 = 24^2

2a^2 = 576

a^2 = 288

a = √288

Now, let's find the height 'h' of the prism. The height 'h' is equal to the radius of the hemisphere, which is 12 cm.

Therefore, the dimensions of the prism for maximum volume are:

Base length (a) = √288 cm

Height (h) = 12 cm

To find the maximum volume, we can use the formula for the volume of a right triangular prism:

Volume = (1/2) * a^2 * h

Substituting the values, we get:

Volume = (1/2) * (√288)^2 * 12

= (1/2) * 288 * 12

= 1728

Hence, the maximum volume of the prism is 1728 cubic centimeters.

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Answer: -1

So I Simplify the expression to the math problem -7+2 +4 = and got -1

The variable P0 represents the initial amount.

In the exponential growth model, P(t) represents the population at time t, P0 represents the initial population at time t=0, k represents the growth rate, and e is the mathematical constant, approximately equal to 2.71828. Therefore, P0 represents the initial amount or the starting point of the population.

The correct answer is B, the variable P0 represents the initial amount.

B. The variable P0 represents the initial amount.

In the exponential growth model P(t) = P0 * e^(kt), the variables are defined as follows:
- P(t): The population size at time 't'
- P0: The initial population size (i.e., the population size at the beginning, when t=0)
- e: The base of the natural logarithm (approximately 2.71828)
- k: The growth rate constant
- t: Time

In this model, P0 is the population size at the beginning of the observed period (when t=0). Therefore, it represents the initial amount.


The variable P0 in the exponential growth model P(t) = P0 * e^(kt) represents the initial amount of the population or quantity being studied.

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Answer:

Step-by-step explanation:

Statement1. ∠KJL ≅∠LMK (A)

Reason1. Given

Statement2. ∠JKL≅∠MLK (A)

Reason2. Given

Statment3. KL≅KL (S)

Reason3. Reflexive propriety

Statemnt 4. ΔJKL≡ΔLMK

Reason 4. AngleAngleSide congruency theorem

Step-by-step explanation:

I know that both sides of the cats, males and females, receive the same # of new cats.

I write an equation, (not an inequality though):

3((34+2x)/5)=2((13+2x)/5)

From here on, I solve for x. I get x = -38. I know we can't have negative pairs and we're only bringing in more cats, and not taking any away. I add 38, and try to see what percentage of cats are male, and I get fairly close, getting to about 62.5% I think. Then, I divide 38 by 2, getting 19, and see what else I can get. I try to find a value between the 38 and lesser 19 so as to find a value which will give me a male cat percentage of 60%. I get about 57.5% with 19 plugged in, which is when I see that hey, the differences are the same. What I then do is find the average of 19 + 38, which is 57.5. I round that to 58, and I get the right answer.

I see that perhaps my solution wasn't really orthodox or anything, but with a little bit of trial and error and a bit of my creative thinking, I guess I managed to solve the problem. What worries me though is this is the first problem in the "questions" section of the inequalities section of AoPS, so I'm definitely struggling to deal with the concepts.

Answer:

2

Explanation:

In short terms, there are two numbers that are reciprocals of themselves, 1 and -1.  According to euler's identity, e^(-i*2*pi) is a reciprocal of itself, but I believe that is beyond the scope of this question.

The final image of the given points after the given translation and dilation of D4,  T3,5 is  (27, -23).

For the given image point of (6, -7) .

First there is a dilation of 4.

Thus,

Image = (6×4 , -7×4)

Image = (24, -28)

Now, there is translation of 3 units right on x axis and 5 unit upward on y axis; T3,5.

Image = (24 + 3, -28 + 5)

Image = (27, -23)

Thus, the final image of the given points after the given translation and dilation is  (27, -23).

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Answer:

3 3/4 cups of sugar

Step-by-step explanation: