What is the value of p ?

The equation in the form Ax+ By=C is 4x-3y=27 if the line passes through the point (-6, 1) and slope is 4/3.

A mathematical formula that connects two expressions with the equals sign (=) expresses the equality of the two expressions. The word equation and its translations in several languages might have slightly different meanings. For instance, in French, an equation is defined as including one or more variables, whereas in English, an equation is defined as any properly expressed formula that consists of two expressions joined by the equals sign.

The values of the variables that must fulfill the equality to make up the solution are referred to as the unknowns, together with the variables for which the equation must be solved.

Given point is (-6, 1)

Slope m=4/3

The equation of the line is:

y-y₁=m(x-x₁)

y-1=(4/3)(x+6)

3y-3=4x+24

4x-3y=27

Therefore, the equation in the form Ax+ By=C is 4x-3y=27

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The algebraic expression represents the result of adding 19 to twice a number is 19 + 2n.

What is an algebraic expression?

An algebraic expression is a combination of numbers, variables, and mathematical operations that can be simplified or evaluated. It is a fundamental concept in algebra, which is the branch of mathematics that deals with the study of symbols and the rules for manipulating them.

To translate the phrase "19 increased by twice a number" into an algebraic expression, we can use the following steps:

Identify the operation being performed: In this case, the phrase "increased by" indicates that we need to use the addition operator (+).

Identify the constants and variables: The constant in this expression is 19, and the variable is "a number", which we will represent with the variable n.

Write the expression: Using the information from steps 1 and 2, we can write the expression as follows:

19 + 2n

Hence, the expression represents the result of adding 19 to twice a number is 19 + 2n.

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The algebraic expression represents the result of adding 19 to twice a number is 19 + 2n.

What is an algebraic expression?

An algebraic expression is a combination of numbers, variables, and mathematical operations that can be simplified or evaluated. It is a fundamental concept in algebra, which is the branch of mathematics that deals with the study of symbols and the rules for manipulating them.

To translate the phrase "19 increased by twice a number" into an algebraic expression, we can use the following steps:

Identify the operation being performed: In this case, the phrase "increased by" indicates that we need to use the addition operator (+).

Identify the constants and variables: The constant in this expression is 19, and the variable is "a number", which we will represent with the variable n.

Write the expression: Using the information from steps 1 and 2, we can write the expression as follows:

19 + 2n

Hence, the algebraic expression represents the result of adding 19 to twice a number is 19 + 2n.

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Answer:

Factored form is (x - 5) (x² + 5x + 25)

Step-by-step explanation:

You can get the factors directly by using the formula for a³ - b³.

Since Amy's rent is 60 percent of the budget for Rent, Utilities, and Food, she will have $853 to spend on entertainment each month.

The total budget for rent, utilities, and food for nine months is given as $12,798.

Using the mathematical operation of multiplication, the proportion that belongs to rent alone is $7,678.80, representing 60%.

This rental proportion is divided by 9 to determine the monthly budget for rent, which will then be spent on entertainment.

The total budget for rent, utilities, and food for nine months = $12,798

The percentage of the budget for rent = 60%

The amount for rent for nine months = $7,678.80 ($12,798 x 60%)

The monthly rent amount is $853.20 ($7,678.80/9)

Thus, we can conclude that Amy will spend $853 monthly on entertainment if she saves the rent budget.

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The percentage of the rent to the total rent, utilities, and food budget is 60%.

The quadratic formula will give us the coordinates of the points of intersection of a line and a quadratic only when the value of the discriminant b^2 - 4ac is either positive or zero .

Given :

the quadratic formula will give us the coordinates of the points of intersection of a line and a quadratic only when the value of the discriminant, is .

Quadratic equation :

Quadratic equations are the polynomial equations of degree 2 in one variable of type f(x) = ax2 + bx + c = 0 where a, b, c, ∈ R and a ≠ 0.

Formula :

= -b ± [tex]\sqrt{b^2 - 4ac / 2a}[/tex]

Discriminant = b^2 - 4ac

if b^2 - 4ac = 0 or positive value then only the formula give us the coordinates of the points of intersection of a line .

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True , a 95% confidence interval for the risk difference for obesity among members of the poor population compared to the affluent population is (-0.03, 0.23).

The critical value for alpha is 0.05 and z is 1.96 .

The corresponding confidence interval is ( 6.235 , 7.165).

Therefore the above statement is true.

Confidence Interval, to put it simply, is a range within which we are confident that the genuine value exists. The probability that a confidence interval will contain the real parameter value depends on the confidence level that is chosen for the interval.

The phrase "Confidence Interval" refers to the range of values that is typically used to handle population-based data, extracting precise, important information with a given level of confidence.

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Answer:

  B.  False

Step-by-step explanation:

You want to know if it is true that a tessellation can be created from circles.

A tessellation is the covering of a plane, using one or more geometric shapes with no overlaps and no gaps.

As the attachment shows, it is not possible to cover a plane with circles, leaving no gaps.

A tessellation cannot be created using circles. The proposition is False.

Gavin should deposit his money into a savings account that is compounded annually at an interest rate of 9%.

What is compound interest?

The interest earned on savings that is computed using both the original principal and the interest accrued over time is known as compound interest.

Given that the current balance is $800.

There were two types of schemes.

First scheme offer compounded annually at an interest rate of 9%

Second scheme offer compounded quarterly at an interest rate of 9%.

The formula of compound interest annually is

A = P(1+r)^t

P = principal = 800

r = rate of interest = 9% = 0.09

t = time = 3 year

A = 800(1+0.09)³

A = 1036.02.

The formula of compound interest annually is

A = P(1+(r/n))^tn

P = principal = 800

r = rate of interest = 3% = 0.03

t = time = 3 year

n = 4

nt = 4×3 =12

A = 800(1+0.03/4)¹²

A = 875.04

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If Liana is indifferent between the bundles (2,6) and (6,2), then it means that she values these two bundles equally. This means that Liana does not have a preference for one bundle over the other.

If Liana's indifference curves are bowed inward, it means that she is willing to give up more units of one good in order to get more units of the other good, as she moves along the indifference curve. This implies that Liana has a diminishing marginal rate of substitution (MRS) between the two goods.

Therefore, if Liana is indifferent between (2,6) and (6,2), it does not necessarily follow that she prefers (4,4) to (6,2). It is possible that Liana may also be indifferent between (4,4) and (6,2), or she may prefer (6,2) to (4,4). This would depend on the specific shape and location of Liana's indifference curves.

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Answer:

[tex]x = -2[/tex]

Step-by-step explanation:

[tex]\textsf {Square both sides:}\\\\(\sqrt{3x+12} )^2 = 3x + 12\\\\(\sqrt{x+8} )^2 = x + 8[/tex]

(The square of the square root of a value is the value itself

[tex](\sqrt{x} )^2 \;is\;x[/tex])

The original identity then becomes
[tex]3x + 12 = x + 8\\\\3x - x = 8 - 12\\\\2x = -4\\\\x = -4/2\\\\x = -2[/tex]

The slope and y intercept of the equation are -6 and 75 respectively.

The slope of a line is a number that describes both the direction and the steepness of the line.

Given that, the equation of a line is y = 75 - 6x

Comparing to the standard equation of the line, y = mx+c

m = slope and c is the y intercept.

In the equation, we can see,

The slope (m) = -6

The y intercept (put x = 0) = y = 75 - 6x0

y = 75

Hence, the slope is -6 and y intercept is 75.

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The multiplications, applying the associative property, are given as follows:

1. (5 x 2) x 3 = 10 x 3 = 30.

2. 4 x (3 x 3) = 4 x 9 = 36.

3. (6 x 1) x 4 = 6 x 4 = 24.

4. 5 x (2 x 4) = 5 x 8 = 40.

5. (2 x 2) x 8 = 4 x 8 = 32.

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

7. (4 x 2) x 4 = 8 x 4 = 32.

8. 6 x (3 x 3) = 6 x 9 = 54.

The associative property of multiplication defines that the order in which the factors are multuiplied does not change the product.

In this problem, we have to consider that the parenthesis gives the precedence of the factors, meaning that the terms inside the parenthesis are multiplied first, and their result should be placed on the blanks below the parenthesis.

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The average speed of the winning car is  79.38 miles per hour.

Given : Distance covered by rally car race course = 515.97 miles

Time taken to complete the course by winning car = 6.5 hours

The average speed of the winning car = ( Distance covered by rally car race course) ÷  (Time taken to complete the course by winning car)

= (515.97)÷ (6.5) miles per hour

= 79.38 miles per hour

Hence, the average speed of the winning car =  79.38 miles per hour.

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The test hypothesis is

H₀: p=0.08 (null hypothesis) and

Hₐ: p<0.08 (alternative hypothesis )

Given that,

8% of adults in the country contract the flu at any given time during a flu epidemic. The following are the hypotheses:

0% of people who received the vaccine contracted the flu.

8% or less of people who received the vaccine ended up getting the flu.

In order to reject the null hypothesis, there must be proof that 8% of individuals who received the vaccine did not also get the flu.

If the null hypothesis is not rejected, then there is insufficient data to draw the inference that the proportion of people who receive the flu shot is 8%.

The test hypothesis is H₀: p=0.08 (null hypothesis) and Hₐ: p<0.08 (alternative hypothesis )

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Answer:

Hi!

If you're trying to solve for z, the answer would be -34.

I hope this helps you :)

Answer:

Below

Step-by-step explanation:

.94 % is .0094 in decimal

   this exponential growth is like a bank account compounded yearly

         factor =  ( 1+.0094)^30  = 1.3240  

                   which would represent 32.40% growth

The greatest number of snack bags is 10.

The largest of all the common factors between two or more numbers is known as the Highest Common Factor (HCF). It is also known as the Greatest Common Element (GCF).

HCF is a fundamental method that allows you to equally distribute items throughout a group or set.

We can use the idea of HCF to determine the same when you are organizing a party and want to make sure that nothing is wasted or you require a proper calculation.

Here we have

Number of carrots = 75

Number of celery sticks = 40

Here we are making snack bags such that each bag contains the same combination of carrot and celery sticks.

To find the greatest number of snack bags we need to find HCF of 70 and 40 as given below

Write given numbers as the product of prime numbers

=> 70 = 2 × 5 × 7

=> 40 = 2 × 2 × 2 × 5  

List out the common factors

=> 2 × 5  

=> HCF (70, 40) = 10

Therefore,

The greatest number of snack bags is 10.

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Answer:

A

Step-by-step explanation:

The answer is option A

Hope this helps :)

Between x=-1 and x=1, the average rate of change is 1.

It represents the average change in the function's per-unit value during that time period. Calculating the average rate of change is very helpful for tracking changes in measurable parameters like average speed or average velocity. As the slope of the straight line that links the two spots, the average rate of change between the two points is determined. Use the formula:

(f(b)-f(a))/(b-a) to get the average rate of change of f(x) between x=a and x=b.

Given line in the figure passes through the points A(4, 0), B(-1, -5)

Let the  equation of the line be:

y=mx+ c

Slope m=(-5-0)/(-1-4)

m=1

Therefore, y=x+ c

It passes through (4, 0)

y+ c=0

c=-4

y=x-4=f(x)

f(-1)= -1-4=-5

f(1)= 1-4=-3

The average rate of change=(f(b)-f(a))/(b-a)

=(f(1)-f(-1))/1-(-1)

= -3-(-5)/(1+1)

=2/2

=1

Therefore, Between x=-1 and x=1, the average rate of change is 1.

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The growth of the mass of the sample of a bacteria is represented by the exponential model m(x) = 5 · 1.02ˣ.

In this problem we find the case of mass of a sample of a bacteria (m(x)), in miligrams growing in time (x), in days. This growth is done exponentially, the exponential model is shown below:

m(x) = m' · (1 + r / 100)ˣ

Where:

We have that the mass of the sample was initially 5 miligrams and grows at a rate of 2 % during 10 days. If we know that m' = 5 mg and r = 2, then the exponential model for the sample is:

m(x) = 5 · 1.02ˣ

The exponential model for the sample of a bacteria is equal to m(x) = 5 · 1.02ˣ.

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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:  [tex]\mathrm{z}=\frac{\overline{\mathrm{x}}-\mu}{\frac{\sigma}{\sqrt{\mathrm{n}}}}\\[/tex]

Where, n = total number of sample = 100

[tex]\bar x[/tex] = mean of the given data

[tex]\mu[/tex] = 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:

[tex]=\frac{99-100}{\frac{6}{\sqrt{260}}}=-1.67[/tex]

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Answer:

The original price of the tie was 20 dollars

Step-by-step explanation:

The price of the t-shirt was originally 24, but because he bought it on sale, he would have payed 12 because 24x.5=12.  This means we can subtract the value payed for the shirt from the total money payed. 22(total)-12(shirt)=.  10 (tie). However, 10 is the price he payed for the tie, not its original value. We can find this by multiplying 10x2, which gives us our answer.

Answer:

20 dollars is the original price

The average distance from a point in the ball to its center = [tex]\frac{3}{4}[/tex] A

Given the radius in the question = a

The integration of the total distance before dividing the volume will be =

⇒ [tex]\int_0^{2\pi}\int_0^\pi\int_0^A a\cdot a^2\sin\theta\,da\,d\theta\,d\phi[/tex]

⇒ [tex]\int_0^{2\pi}\int_0^\pi\int_0^A a^3\sin\theta\,da\,d\theta\,d\phi[/tex]

⇒ [tex]\frac{A^{4} }{2}[/tex] [tex]\int_0^{2\pi}\int_0^\pi \sin\theta\,d\theta\,d\phi[/tex]

⇒ [tex]\frac{A^{4} }{2}[/tex] [tex]\int_0^{2\pi}1\,d\phi[/tex]

⇒ [tex]\pi A^{4}[/tex]

Let us divide the average distance by the ball's volume,

⇒ [tex]\frac{\pi a^4}{(4/3)\pi a^3}[/tex]

⇒ [tex]{\frac{3a}4}[/tex]

By the use of the Parcly Taxel's way,

Let the radius of the ball be = A

f(x) = probability density function

Distance = D from the given point to the center.

P( D < a )

[tex]\begin{align}P(D\leq r)&= \frac{ \frac 43 \pi r^3 }{\frac 43 \pi R^3}=\frac {r^3}{R^3}, \ \ \ 0\leq r\leq R. \end{align}[/tex][tex]\frac{\frac{4}{3} \pi a^{3} }{\frac{4}{3} \pi A^{3} } = \frac{a^{3} }{R^{3} }[/tex]. 0 [tex]\leq[/tex] a [tex]\leq[/tex] A

Therefore, The average distance from a point in the ball to its center = [tex]\frac{3}{4}[/tex] A

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The statement "Return on equity will not change if the firm increases its use of debt" is false.

Return on equity (ROE) is a financial ratio that shows how well a company is managing the capital that shareholders have invested in it. To calculate ROE, one would divide net income by shareholder equity.

Given is a statement, "Return on equity will not change if the firm increases its use of debt".

As we know that, The equity equals the assets minus total debt, a company decreases its equity by increasing the debt, or we can say, when debt increases, the equity decreases and since equity is ROE's denominator, ROE in turns gets a boost.

Hence, the statement "Return on equity will not change if the firm increases its use of debt" is false.

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The area of each section is 3/4 square feet. To solve the give question use division operation.

What is mixed fraction?

A mixed fraction is one that is represented by both its quotient and remainder. A mixed fraction is, for instance, 2 1/3, where 2 is the quotient and 1 is the remainder.

Given that the area of the garden is [tex]5\frac{1}{4}[/tex] square feet.

Now convert the mixed fraction with improper fraction:

[tex]5\frac{1}{4}[/tex] = [(5×4) + 1]/4

[tex]5\frac{1}{4}[/tex] = 21/4

We have to divide the area 7 equal area.

Thus divide 21/4 by 7.

21/4 ÷ 7

To convert the division sign into multiplication sign, take the reciprocal of 7:

21/4 × 1/7

= (21 × 1)/(4 × 7)

Divide the denominator and numerator by 7:

= 3/4

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After using trigonometric function the value of to the nearest tenth digit is 11.11

What is Trigonometric function ?

Trigonometric functions are mathematical functions that are used to describe relationships between certain angles and lengths in a triangle. They are based on the ratios of the sides of a right triangle and are used in a variety of applications including surveying, navigation, engineering, and physics. Trigonometric functions are commonly referred to as sine, cosine, tangent, cotangent, secant, and cosecant. Each of these functions can be used to calculate the angle of a triangle, the length of the sides, or the area of the triangle.

Function of Sine

The ratio of the opposing side's length to the hypotenuse is known as an angle's sine function.
Sin a =Opp/Hypot = CB/CA

Cos Function
The cosine of an angle is the ratio of the neighbouring side's length to the hypotenuse's length.
Adjacent/Hypotenuse = AB/CA is the cosine of.

Functional Tan
The ratio of the lengths of the adjacent and opposing sides is known as the tangent function. It should be noted that the ratio of sine and cosine to the tan may also be used to express the tan.
Tan a = Opposite/Adjacent = CB/BA
In terms of sine and cos, tan is also equivalent to:
Tan = cos a/sin a
Sin 46° = 8/x
x = 8/Sin 46°
x= 8/0.72
x=11.11

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Answer:

4

Step-by-step explanation:

let n be the integer , then n tripled is 3n, so

[tex]\frac{3}{4}[/tex] n + 9 = 3n ( multiply through by 4 to clear the fraction )

3n + 36 = 12n ( subtract 3n from both sides )

36 = 9n ( divide both sides by 9 )

4 = n

the required integer is 4