9) Give the following expression in index form
a) √3

Answer:

a.

Equation 1: y = x + 1

Equation 2: y = 4x - 5

Substitute Equation 1 into Equation 2:

x + 1 = 4x - 5

Now, solve for x:

4x - x = 1 + 5

3x = 6

x = 2

So now we have x, lets solve for y:

y = x + 1

Substitute x:

y = 2 + 1

y = 3

So the point of intersection of line y = x + 1 and line y = 4x -5 is (2,3) as shown on the graph.

Lets do the other two now:

b.

Equation 1: x + 4y = 1

Equation 2: 2x - y = -7

For this one we cannot simply substitute we have to get rid of one variable to create another equation.

Lets get rid of x for equation 3. To do this we simply times Equation 1 by 2:

Equation 3: 2x + 8y = 2

With this we can minus Equation 2 and Equation 3 to get rid of x:

2x - y = -7

-

2x + 8y = 2

-9y = -9

y = 1

Now that we have the y value, we can now find x using any equations above, lets use Equation 1:

x + 4y = 1

x + 4(1) = 1

x + 4 = 1

x = 1 - 4

x = -3

So the point of intersection is (-3,1).

c.

Equation 1: 4x + y = 11

Equation 2: y = -2x + 3

For this question, we can just do what we did for question a.

Lets substitute Equation 2 into Equation 1:

4x + (-2x + 3) = 11

4x - 2x + 3 = 11

2x + 3 = 11

2x = 11 - 3

2x = 8

x = 4

So we got our x value, let get our y value. Lets use Equation 1 for that:

4x + y = 11

4(4) + y = 11

16 + y = 11

y = 11 - 16

y = -5

So, the point of intersection is (4,-5).

Using the concepts of unitary method, we got that  $42.83 was the total for all of the food and drink. if me and my friend went to dinner together and ordered 4 hamburgers at $5.95 each, 3 baskets of fries at $4.25 each, and 4 sodas at $1.75 each

Since, we are given that cost price of one hamburger is $5.95,

so total cost of 4 hamburgers is =4×5.95=$23.08

Similarly, we are given that cost price of one baskets of fries which is $4.25,

so total cost of three baskets of fries is =3×4.25=$12.75

Similarly, we are given that cost price of one soda which is $1.75,

so total cost of 4 soda  is =4×1.75=$7.00

So, Total cost of my order is= 4 hamburger cost+3 baskets of fries cost +4 sodas cost =23.08+12.75+7.00=$42.83

Hence, if me and my friends went to dinner together and ordered 4 hamburgers at $5.95 each, 3 baskets of fries at $4.25 each, and 4 sodas at $1.75 each, the total for all of the food and drink was $42.83

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Answer:

729! Hope this helps :)

Step-by-step explanation:

Answer:

9^3 in standard form

Step-by-step explanation:

9 × 9 × 9

81 × 9

729

The measure of the angle SQR is 68 degrees if m/PSR = 134 and Angle QPS = Angle PSQ  = Angle SQP = 60 degrees.

When two lines or rays converge at the same point, the measurement between them is called a "Angle."

It is given that:

m/PSR = 134,

PQ = QS = PS

Angle QPS = Angle PSQ  = Angle SQP = 60 degrees

Angle QSR = QRS

Angle SQR = 180 - (180 - 134)x2

= 180 - 112

= 68 degrees

Thus, the measure of the angle SQR is 68 degrees if m/PSR = 134 and Angle QPS = Angle PSQ  = Angle SQP = 60 degrees.

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[tex]~~~~~~ \textit{Compound Interest Earned Amount} \\\\ A=P\left(1+\frac{r}{n}\right)^{nt} \quad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{original amount deposited}\dotfill &\$500\\ r=rate\to 4\%\to \frac{4}{100}\dotfill &0.04\\ n= \begin{array}{llll} \textit{times it compounds per year}\\ \textit{quarterly, thus four} \end{array}\dotfill &4\\ t=years\dotfill &5 \end{cases} \\\\\\ A=500\left(1+\frac{0.04}{4}\right)^{4\cdot 5} \implies A=500(1.01)^{20}\implies A \approx 610.10[/tex]

When testing the difference between two population means, the sample variances are pooled to estimate the population variance when The population variances are assumed equal but unknown.

Population Mean:

The population mean can be calculated by the sum of all values in the given data/population divided by a total number of values in the given data/population.

In testing for the differences between the means of two independent populations where the variances in each population are unknown but assumed equal, the degrees of freedom are: n1 + n2 - 2.

population variance:

Population variance is a measure of how spread out a group of data points is. Specifically, it quantifies the average squared deviation from the mean.

Therefore When testing the difference between two population means, the sample variances are pooled to estimate the population variance when The population variances are assumed equal but unknown.

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Answer:

x=7/10

Step-by-step explanation:

Because this is a square, we know that all of the sides are equal.

Thus, we know that 6x-1=4x+6.

We can further use Algebra and subtract by 4x on both sides.

Now, we have 10x-1=6.

Then, we can add 1 to both sides, and get 10x=7.

Lastly, let's divide both sides by 10 to isolate x, getting x=7/10, or x=0.7

If the equation is 4y - 6x = 12, then (-4, -3) and (0, 3) are the solutions of the equation

The equation is given that

4y - 6x = 12

The first solution =(-4, -3)

The value of x = -4

The value of y = -3

Substitute the values in the equation

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

-12 - (-24) = 12

-12 + 24 = 12

12 = 12

Therefore (-4, -3) is the solution of the equation

Next solution is (0, 3)

The value of x = 0

The value of y = 3

Substitute the values in the equation

4(3) - 6(0) = 12

12 - 0 = 12

12 = 12

Therefore (0, 3) is the solution of the equation

Hence, if the equation is 4y - 6x = 12, then (-4, -3) and (0, 3) are the solutions of the equation

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Answer: x = 7

Step-by-step explanation: 6x = x^2 - 7

x^2 - 6x -7 =0

(x-7) (x+1) = 0

x = 7  

x = -1 ----> rejected

The positive solution of the required number is 7.

An expression is a grouping of one or more mathematical or logical operators, operands (values, variables, or other expressions), and brackets in mathematics and computer programming that denote a computation that can be evaluated to generate a value.

Let's start by translating the given sentence into an equation. Let "x" be the number we are trying to find. Then we can write:

6x = x² - 7

Now we need to solve for x. Let's rearrange the equation to get all the x terms on one side and all the constant terms on the other side:

x² - 6x - 7 = 0

We can solve this quadratic equation by factoring or using the quadratic formula, but let's use factoring for this problem. We need to find two numbers whose product is -7 and whose sum is -6. The two numbers are -7 and 1, so we can write:

(x - 7)(x + 1) = 0

This means that either x - 7 = 0 or x + 1 = 0. Solving for x, we get:

x = 7 or x = -1

Since we are looking for a positive solution, the answer is x = 7. Therefore, the positive solution is 7.

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As per the given system of linear equation, the number of solution is infinite.

Linear equations:

An algebraic equation of the form

y = mx + b

Involving only a constant and a first-order (linear) term, where m is the slope and b is the y-intercept is known as linear equation.

Given,

A system of three linear equations in three variables is consistent and dependent.

Here we need to find the number of solution for this system.

Here we know that the given system of three linear equations in three variables which is consistent and dependent.

We know that, the system is said to be consistent if it has at least one solution. Which means that the system which has no solution is said to be inconsistent.

Similarly, the system is has consistent solution is said to be independent if it has only one solution whereas it is said to be dependent if it has an infinitely many solutions.

Therefore, here the given system of three linear equations in three variables which is consistent and dependent, the system has an infinitely many solutions.

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The mean length of time for each missed appointment in minutes will be 13.2 minutes per missed appointment.

The mean is the simple definition of the average of a large number. This actually implies one of the indicators of focused tendency in measurements. The statistic means is referred to as the normal. It is the ratio of the number of true judgments to the total number of impressions.

This sign was in a specialist's sitting area. 115 arrangements were missed a month ago. These missed arrangements were a sum of 25.3 hours.

The total number of minutes is given as,

⇒ 25.3 hours

⇒ 25.3 x 60 minutes

⇒ 1,518 minutes

The mean length of time for each missed appointment in minutes will be given as,

⇒ 1,518 / 115

⇒ 13.2 minutes per missed appointment

The mean length of time for each missed appointment in minutes will be 13.2 minutes per missed appointment.

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Answer:

$2300

Step-by-step explanation:

1. Her yearly allowable debt

36% × 85000 = 30600

2. Her monthly allowable debt

30600/12 = 2550

3. Her monthly existing debt

car payment = 200

car insurance = 300/6 =50

monthly utility bill = na this is an estimation

4. allowable debt - existing debt

2550 -200-50= 2300

ps: i may be wrong

A Paired t-test evaluates data from dependent samples in which the two

treatments are applied to the same individual.

T-test is a statistical statistics mainly use when population variance is

unknown and sample size is small.

In Paired t-test , we compare means of two dependent samples. It gives

hypothesis examination on difference between of mean.

It uses same items or people in both sample that's why they are also known as dependent t-test or Paired t-test also increases the statistical power of our analysis.

Formula of paired t-test :

t = m / S / n

with (n-1) degree

where , m --> mean difference

S ---> standard deviation difference

n --> sample size

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Since they take prices rather than setting them, fully competitive enterprises must deal with a completely elastic demand curve.

What is competitive firm?

A perfectly competitive firm is a price taker, which means that it must accept the equilibrium price at which it sells goods. If a perfectly competitive firm attempts to charge even a tiny amount more than the market price, it will be unable to make any sales.

Since they take prices rather than setting them, fully competitive enterprises must deal with a completely elastic demand curve. They are so unable to alter the market selling price. In order to raise its income, a perfectly competitive firm will therefore increase output rather than pricing.

A totally competitive firm is unable to arbitrarily set its output price since it must accept the price set by the product's market demand and supply. As an alternative, the perfectly competitive firm can decide to sell any amount of output for the same price. Because customers are eager to purchase any quantity of the company's output at the market price, it follows that the firm must deal with a completely elastic demand curve for its product. The quantity that the perfectly competitive firm decides to produce, combined with the prices that are in effect on the market for inputs and outputs, will determine the firm's total revenue, total costs, and eventually the level of profits.

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The y-intercept of the equation means: D. It means the technician charges a fixed amount of $50 for the repair.

The y-intercept of an equation that models a situation is the initial or starting value. The y-intercept is represented in an equation that is expressed in slope-intercept form, y = mx + b, as "b". The value of "b" is the y-intercept.

Therefore, we are given that y = 20x + 50 represents the total amount the technician charges, in dollars, for a repair that takes specific hours. This implies that:

Therefore, y-intercept, b = 50, means: D. It means the technician charges a fixed amount of $50 for the repair.

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The polynomial representing length, breadth and height of th e container is

Volume is measure in liters, cubic meters and so on

The formula for volume calculation is given by

volume = length * width * height

from the question

height is 0.15 m more than their width

width = w

height = 0.15 + w

length = L

volume = 652 m³

652 = L * w * (w + 0.15)

652 = (w^2 + 0.15w)L

652 = Lw^2 + 0.15Lw

Lw^2 + 0.15Lw - 652

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Answer:

10

Step-by-step explanation:

tbh i am confused

please if you see this, i am really trying my best and you guys gave me the hardest question i ever had. sincerely apologize

Step-by-step explanation:

item on sale costs 60 % of the original price

(sale price) = 60% of (original price)

(sale price) = 60% of $85

[given: (original price) = $85

(sale price) = $(60/100)*85

[60% may be written as 60/100 or 0.60 as needed by the problem]

(sale price) = $51.00

Answer: ?

Step-by-step explanation:

that's how you do it.

Answer: $14

Step-by-step explanation:

First, find the amount it will cost with one guest(x):

[tex]\frac{10}{5} =\frac{x}{1} \\\\10=5x\\\\x=\frac{10}{5} =2[/tex]

Then, use ratios to find the amount it will cost with seven guests(y):

[tex]\frac{2}{1} =\frac{y}{7} \\\\y=14[/tex]

Not sure if this is how you want it to be solved.

Answer:

[tex]u=-25.6[/tex]

Step-by-step explanation:

Take a look at the attachment...

Hope this helps! :)

Answer:

h = 9

Step-by-step explanation:

Step 1: Subtract 6h from both sides.

4h +3 −6h = 6h −15 −6h

−2h +3 = −15

Step 2: Subtract 3 from both sides.

−2h + 3 −3 = −15 −3

−2h = −18

Step 3: Divide both sides by -2.

(-2h/-2) = (-18/-2)

h = 9

Answer:

x has no real solution/roots

Step-by-step explanation:

please see the attached image:

The probability that the sample proportion will be greater than 0.78 is:

78% of 400 is 0.78× 400 = 312.

So this probability is 1 subtracted by the p value of Z when x = 312

Z = (X - μ)/σ

We are going to approximate the binomial distribution to the normal.

Binomial probability distribution-

Probability of exactly x sucesses on n repeated trials, with p probability.

Can be approximated to a normal distribution, using the expected value and the standard deviation.

The expected value of the binomial distribution is:

E(X) = np

The standard deviation of the binomial distribution is:

√V(X) = √np(1 - p)

Normal probability distribution-

Problems of normally distributed samples can be solved using the z-score formula.

In a set with mean and standard deviation o, the zscore of a measure X is given by:

Z = (X-μ)/σ

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z- score table and find the p-value 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. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

When we are approximating a binomial distribution to a normal one, we have that-

μ = E (X), σ = √V√(X).

In this problem, we have that:

n=400, p=0.8

So = E(X)=np=400-0.8=320

σ = √V(X) = √np(1-p)=√400×√0.8×√0.2=8

Hence, the probability that the sample proportion will be greater than 0.78 is:

78% of 400 is 0.78× 400 = 312.

So this probability is 1 subtracted by the p value of Z when x = 312

Z = (X - μ)/σ

Z = (312- 320)/8.

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Answer:

the answer is either x= 4 , or it is   9[tex]x^{2} \\[/tex] - [tex]x[/tex] - 10

Step-by-step explanation:

Sorry dude, I'm confused a little bit on what to do, but i think one of these is right.

lmk if you get it right, and which one you used

Answer:

3√13

Step-by-step explanation:

4 : y = y = 9

y^2 = 36

y = 6

z = [tex]\sqrt{9^2 + 6^2} = \sqrt{81 + 36} = \sqrt{117}[/tex]

117 = 3^2 * 13

[tex]\sqrt{117} = \sqrt{3^2 * 13} = 3\sqrt{13[/tex]

Answer:

[tex]16x^4y^2 a^6[/tex]

Step-by-step explanation:

[tex](-4x^2ya^3)^2=(-4)^2(x^2)^2(y)^2(a^3)^2 \\ \\ =16x^4y^2 a^6[/tex]

The expression can be written without negative exponents as 1/(bm)³

Exponent is defined as the method of expressing large numbers in terms of powers. That means, exponent refers to how many times a number multiplied by itself. For example, 6 is multiplied by itself 4 times, i.e. 6 × 6 × 6 × 6. This can be written as 6⁴. Here, 4 is the exponent and 6 is the base.

Simplifying exponents is a method of simplifying the algebraic expressions involving exponents into a simpler form such that they cannot further be simplified. There are rules in algebra for simplifying exponents with different and same bases that we can use.

Steps to removing exponents are;

Step 1

remove parentheses by multiplying factors.

Step 2

use exponent rules to remove parentheses in terms with exponents.

Step 3

combine like terms by adding coefficients.

Step 4

combine the constants.

In this case, we have an expression;

(bm)⁻³ which can be rewritten using cube.

(bm)⁻³ = 1/ (bm)³

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Answer:

Step-by-step explanation:

First calculate 55% of 150:

= 150 x 55/100

= 82.5 ans

Now decrease it from 150:

= 150-82.5

= 67.5 ans Hope it helps!!

Answer:

9. train a = 8.33 hours

train b = 5 hours

time of coincidence = 3.33 hours

Step-by-step explanation:

I'm not sure about this but I think it's correct.