Zaire is buying a truck that costs p dollars. The expression shown represents the sales tax on the truck.
0.07 p
Which expression in terms of p, represents the total price of the truck including sales tax?
0 2p +0.07
p=0.07
0 107p
0 0.07 p

Answer:

y = 2x - 7

Step-by-step explanation:

the equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

here m = 2 , then

y = 2x + c ← is the partial equation

to find c substitute (2, - 3 ) into the partial equation

- 3 = 2(2) + c = 4 + c ( subtract 4 from both sides )

- 7 = c

y = 2x - 7 ← equation of line

Answer:

4^4

Step-by-step explanation:

The equation of the path of the parabola is y = a(x - 13)² + 27

Given data ,

To represent the path of Al's toss, we can assume that the path is a parabolic trajectory.

The equation of a parabola in vertex form is given by:

y = a(x - h)² + k

where (h, k) represents the vertex of the parabola

Now , the balloon was released from the 10-yard line and landed at the 16-yard line, we can determine the x-values for the vertex of the parabola.

The x-coordinate of the vertex is the average of the two x-values (10 and 16) where the balloon was released and landed:

h = (10 + 16) / 2 = 13

Since the height of the balloon reached 27 yards, we have the vertex point (13, 27)

Now, let's substitute the vertex coordinates (h, k) into the general equation:

y = a(x - 13)² + k

Substituting the vertex coordinates (13, 27)

y = a(x - 13)² + 27

To determine the value of 'a', we need another point on the parabolic path. Let's assume that the highest point reached by the balloon is the vertex (13, 27).

This means that the highest point (13, 27) lies on the parabola

Substituting the vertex coordinates (13, 27) into the equation

27 = a(13 - 13)² + 27

27 = a(0) + 27

27 = 27

Hence , the equation representing the path of Al's toss is y = a(x - 13)² + 27, where 'a' can be any real number

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he blank spaces in the given statements represent the amounts received by preferred stockholders and common shareholders in terms of dividends in each scenario.

In year 1, with 20,000 shares of preferred stock and $10,000 in dividends, to determine the amount received by preferred stockholders (fill in the blank 1), For common shareholders (fill in the blank 2), since they receive the remaining dividends after preferred stockholders are paid, the amount would be $10,000 - (20,000 * $0.50).

In year 2, with 20,000 shares of preferred stock and $10,000 in dividends paid in year 1, For common shareholders (fill in the blank 4), the amount would be $45,000 minus the dividends received by preferred stockholders in year 2.

In year 1, with 25,000 shares of preferred stock and $18,000 in dividends, the calculation for preferred stockholders (fill in the blank 5) is $18,000 / 25,000 per share. The amount received by common shareholders (fill in the blank 6) would be $18,000 minus the dividends received by preferred stockholders.

In year 2, with 25,000 shares of preferred stock and $18,000 in dividends paid in year 1, and an additional $45,000 in dividends paid, the calculation for preferred stockholders (fill in the blank 7) is the same as before, which is $18,000 / 25,000 per share. The amount received by common shareholders would be $45,000 minus the dividends received by preferred stockholders in year 2.

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Answer:

i will tell u if u give me brain liest

Step-by-step explanation:

Step-by-step explanation:

\( f(x) = - 3 {x}^{2} + 9x - 2\)

A) f(-2) + f(1) = -32 + 4 = -28

B) f(-2) - f(1) = -32 - 4 = -36

Answer:

42 Square feet

Step-by-step explanation:

A=(1/2)bh

A=(1/2)(14)(6)

A=42

The probability that two consonants and one vowel are chosen is 0.536.

Probability determines the chances that an event would happen. The probability the event occurs lies between 0 and 1.  

The probability that two consonants and one vowel =( \(\frac{5!}{3!2!} . \frac{3!}{2!1!}\)) ÷ \(\frac{8!}{3!5!}\) = 0.536

Here is the complete question: The word geometry has eight letters. three letters are chosen at random. what is the probability that two consonants and one vowel are chosen? 0.536 0.268 0.179 0.089

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Answer:

A

Step-by-step explanation:

cuz yes

Step-by-step explanation:

v=u+at

v=2+(-5)1

2

v=2-2.5

v=-0.5m/s²

hope it helps.

Answer:

\(v = u + at \\ v = 2 + ( - 5)( \frac{1}{2} ) \\ v = 2 + \frac{( - 5)}{2} \\ v = \frac{4 + ( - 5)}{2} \\ v = \frac{ (- 1)}{2} \\ v = - 0.5 \: m {s}^{ - 1} \)

You will be required to pay $130.92 in interest. So, option 2 is correct.

Simple interest is calculated using the following formula: Simple Interest (SI) is calculated as P R T / 100. P stands for the principal sum, R for the interest rate, and T for the interest period. The total amount due is the sum of the principal plus the simple interest, or P + SI.

This specific percentage represents the loan's interest rate. The cost of borrowing money is called interest, and it is usually expressed as a percentage, such as an annual percentage rate (APR). Interest may be paid to lenders for the use of their money.

You shell out $875.00 for a PC plus 5% sales tax.

Thus, the final price is 875+(0.05875)

= $918.75.

Rate per month: 14.25/12/100

= 0.011875

So, the rate for a year is 12 x 0.011875

=$130.92.

Therefore, you will be required to pay $130.92 in interest.

Hence, option 2 is correct.

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B1. the bottle would contain less than 36 oz approximately 20.33% of the time when the machine is set at 37 oz.

B2. The bottles will overflow approximately 4.75% of the time when the machine is set at 38 oz.

B3. The probability that at least one bottle will overflow out of 10 bottles filled when the machine is set at 38 oz is approximately 99.9%.

B4. The probability that exactly 3 bottles will overflow out of 15 bottles filled when the machine is set at 38 oz is approximately 25.0%.

B5. The bottle would need to be approximately 40.796 oz or larger to avoid overflowing 99.8% of the time when the machine is set at 38 oz.

B1. To find the percentage of time the bottle contains less than 36 oz when the machine is set at 37 oz, we need to calculate the probability that a random bottle will have a volume less than 36 oz.

Using the normal distribution, we can calculate the z-score (standardized score) for 36 oz using the formula:

z = (x - μ) / σ

where x is the desired value (36 oz), μ is the mean of the process (37 oz), and σ is the standard deviation (1.2 oz).

z = (36 - 37) / 1.2

z ≈ -0.833

Using a standard normal distribution table or a statistical calculator, we can find the cumulative probability associated with this z-score.

P(X < 36) = P(Z < -0.833) ≈ 0.2033

Therefore, the bottle would contain less than 36 oz approximately 20.33% of the time when the machine is set at 37 oz.

B2. To find the percentage of time the bottles will overflow when the machine is set at 38 oz, we need to calculate the probability that a random bottle will have a volume greater than 40 oz.

Using the normal distribution, we can calculate the z-score for 40 oz using the formula mentioned earlier:

z = (x - μ) / σ

z = (40 - 38) / 1.2

z ≈ 1.67

Using a standard normal distribution table or a statistical calculator, we can find the cumulative probability associated with this z-score.

P(X > 40) = P(Z > 1.67) ≈ 0.0475

Therefore, the bottles will overflow approximately 4.75% of the time when the machine is set at 38 oz.

B3. To find the probability that at least one bottle will overflow out of 10 bottles filled when the machine is set at 38 oz, we can use the complement rule and subtract the probability that none of the bottles overflow.

The probability of no overflow in a single bottle is given by:

P(X ≤ 38) = P(Z ≤ (38 - 38) / 1.2) = P(Z ≤ 0) ≈ 0.5

Therefore, the probability of no overflow in 10 bottles is:

P(no overflow in 10 bottles) = (0.5)¹⁰ ≈ 0.00098

The probability that at least one bottle will overflow is the complement of no overflow:

P(at least one overflow in 10 bottles) = 1 - P(no overflow in 10 bottles) ≈ 1 - 0.00098 ≈ 0.999

Therefore, the probability that at least one bottle will overflow out of 10 bottles filled when the machine is set at 38 oz is approximately 99.9%.

B4. To find the probability that exactly 3 bottles will overflow out of 15 bottles filled when the machine is set at 38 oz, we can use the binomial distribution formula:

P(X = k) = (nCk) * \(p^k * (1 - p)^{(n - k)\)

where n is the number of trials (15), k is the desired number of successes (3), p is the probability of success (probability of overflow), and (nCk) is the number of combinations.

Using the probability of overflow calculated in B2:

p = 0.0475

The number of combinations for selecting 3 out of 15 bottles is given by:

15C3 = 15! / (3! * (15 - 3)!) = 455

Plugging the values into the binomial distribution formula:

P(X = 3) = 455 * (0.0475)³ * (1 - 0.0475)¹² ≈ 0.250

Therefore, the probability that exactly 3 bottles will overflow out of 15 bottles filled when the machine is set at 38 oz is approximately 25.0%.

B5. To determine the required size of the bottle to avoid overflowing 99.8% of the time when the machine is set at 38 oz, we need to find the z-score corresponding to a cumulative probability of 0.998.

Using a standard normal distribution table or a statistical calculator, we find the z-score for a cumulative probability of 0.998 to be approximately 2.33.

Using the formula mentioned earlier:

z = (x - μ) / σ

Substituting the known values:

2.33 = (x - 38) / 1.2

Solving for x:

x - 38 = 2.33 * 1.2

x - 38 ≈ 2.796

x ≈ 40.796

Therefore, the bottle would need to be approximately 40.796 oz or larger to avoid overflowing 99.8% of the time when the machine is set at 38 oz.

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The first 3 terms of the sequence are 21, 24 and 29

From the question, we have the following parameters that can be used in our computation:

n² + 20

This means that

f(n) = n² + 20

The first 3 terms of the sequence is when n = 1, 2 and 3

So, we have

f(1) = 1² + 20 = 21

f(2) = 2² + 20 = 24

f(3) = 3² + 20 = 29

Hence, the first 3 terms of the sequence are 21, 24 and 29

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23-8x+5x+1

23-3x+1

24-3x

Answer: -3x+24

Answer:

I belive (8,10)

Step-by-step explanation:

8 is 4 twice

10 is 5 twice

For the angular velocity of the gear, you'll need to gather relevant information about the gear, calculate the linear velocity, and use the formula = v / r. The velocity of the center "O" is always 0 as it does not move linearly.

To determine the angular velocity and the velocity of the center 'O' of the gear at the given instant, you will need to follow these steps:

Step 1: Identify the relevant information.
First, gather information about the gear, such as its radius, the speed at which it is rotating, and any other relevant details. To determine the angular velocity of the gear and the velocity of its center at the instant shown, we need to know the radius of the gear and the speed of its rotation. The angular velocity of the gear can be calculated by dividing the speed of rotation by the radius of the gear. The velocity of the center of the gear can be calculated by multiplying the angular velocity by the radius of the gear.

Step 2: Calculate the angular velocity.
Angular velocity () can be calculated using the formula  = v / r, where 'v' is the linear velocity at the edge of the gear and 'r' is the radius of the gear.

Step 3: Find the linear velocity at the edge of the gear.
This can typically be given or can be determined based on the information provided.

Step 4: Calculate the angular velocity.
Plug the values of linear velocity (v) and radius (r) into the formula  = v / r to find the angular velocity.
Angular velocity = (speed of rotation) / (radius of gear)
Velocity of center = (angular velocity) x (radius of gear)

Step 5: Determine the velocity of the center 'O'
Since the center 'O' of the gear is the point around which the gear rotates, its velocity is 0, as it does not move linearly.

In summary, to find the angular velocity of the gear, you'll need to gather relevant information about the gear, calculate the linear velocity, and use the formula  = v / r. The velocity of the center "O" is always 0 as it does not move linearly.

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Answer:

It makes the calculation easy and quick.

Step-by-step explanation:

When you multiply as it is given:

Using the commutative property makes it much easier:

Answer:

see below.

Step-by-step explanation:

its a commutative property of multiplication.

it doesn't matter in order or not... the result will always be the same.

form your example 5×87×2, if you use a calculator it doesn't matter which number you start.

say 2 x 87 x 5 = 870

or 87 x 5 x 2 = 870

or 5 x 2 x 87 = 870

see the results are all the same no matter which way you go.

The 90% confidence interval for the proportion of district residents in favor of starting the school day 15 minutes later is (0.392, 0.548). The true proportion is estimated to lie within this interval with 90% confidence.

To calculate the 90% confidence interval for the true proportion of district residents who are in favor of starting the school day 15 minutes later, we can use the following formula:

CI = p ± z*(√(p*(1-p)/n))

where:

CI: confidence interval

p: proportion of residents in favor of starting the day later

z: z- score based on the confidence level (90% in this case)

n: sample size

First, we need to calculate the sample proportion:

p = 94/200 = 0.47

Next, we need to find the z- score corresponding to the 90% confidence level. Since we want a two-tailed test, we need to find the z- score that cuts off 5% of the area in each tail of the standard normal distribution. Using a z-table, we find that the z- score is 1.645.

Substituting the values into the formula, we get:

CI = 0.47 ± 1.645*(√(0.47*(1-0.47)/200))

Simplifying this expression gives:

CI = 0.47 ± 0.078

Therefore, the 90% confidence interval for the true proportion of district residents who are in favor of starting the school day 15 minutes later is (0.392, 0.548). We can be 90% confident that the true proportion lies within this interval.

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Answer: 3(1-4x)

Step-by-step explanation: if you distribute the answer, you will get 3-12x.

Have a nice day!

The number of minutes Deon will run is equal to or more than 40 minutes if he will run at least 8 laps today.

The possible number of minutes he will run can be determined using inequality.

Inequality is a relation used in mathematics that represents a non-equal comparison between two numbers or any other mathematical expression.

As he runs each lap in 5 minutes and will run at least 8 laps, therefore,

n/5 ≥ 8

Here n represents the number of minutes he will run.

Solving for n;

n ≥ 8 × 5

n ≥ 40

Therefore, the number of minutes he will run is equal to or more than 40 minutes if he will run at least 8 laps today.

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Answer:

x=12

Step-by-step explanation:

10x-18+6x+6=180

16x-12=180

16x=180+12

16x=192

x=192/16

x=12

plz mark as brainliest

the answer is c

Step-by-step explanation:

The length of WY to the nearest 100th is 1.98.

We can start by using trigonometry to find the length of WY. Since we know that ∠Y = 90° and ∠ZWY = 67°, we can use the fact that the angles in a triangle add up to 180° to find that ∠Z = 23°.

Next, we can use the fact that tan(θ) = opposite/adjacent in a right triangle to find the length of WY. In this case, we want to find the length of WY, which is the opposite side to the angle θ = ∠XZW.

First, we need to find the length of the adjacent side XZ. We can use the fact that sin(θ) = opposite/hypotenuse and cos(θ) = adjacent/hypotenuse to find the length of XZ.

sin(9°) = XZ / XW

XZ = XW × sin(9°)

XZ ≈ 0.62

cos(9°) = XZ / XW

XZ = XW × cos(9°)

XZ ≈ 3.57

Now that we know the lengths of XZ and XW, we can find the length of WY.

tan(θ) = opposite/adjacent

tan(67°) = WY / XZ

WY = XZ × tan(67°)

WY ≈ 1.98

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Answer:

Commutative Property of addition

Step-by-step explanation:

The right answers are for Cartesian equation is   \(a =\frac{1}{16},\) \(b = \frac{5}{4}\) , \(c = \frac{25}{4}\) . A parameter is a constant number that controls the output or behavior of a mathematical entity. Parameters and variables are closely connected, and also the distinction is occasionally merely a question of perspective.

We are given:

\(x=t^{2} \\ y=10+4t\)

Rearrange the parametric equation \(y = 10+4t\)

\(y -10=10+4t-10\)

\(y - 10 = 4t\)

\(\frac{y - 10 }{4} = \frac{4t}{4}\)

\(\frac{y - 10}{4} =t\)

\(t = \frac{y - 10}{4}\)

Simplify the descriptive formula by substituting the determined value for \(x= t^{2}\)

Comparing the obtained cartesian equation with \(x=ay+by+c\), the required coefficients are

\(a =\frac{1}{16}\)

\(b = \frac{5}{4}\)

\(c = \frac{25}{4}\)

In mathematics, a parameter is a variable whose range of potential values indicates a group of unique situations in a problem. A parametric solution is any calculation that is represented in terms of variables.

What exactly are parameters and variables?

Variables are quantities that differ from one person to the next. Parameters, on the contrary hand, don't really refer to direct measurements or traits, instead referring to values that define a computational foundation.

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Answer:

The answer is c

Step-by-step explanation:

Answer:

The mortgage chosen is option A;

15-year mortgage term with a 3% interest rate because it has the lowest total amount paid over the loan term of $270,470

Step-by-step explanation:

The details of the home purchase are;

The price of the home = $275,000

The mode of purchase of the home = Mortgage

The percentage of the loan amount payed as down payment = 20%

The amount used as down payment for the loan = $55,000

The principal of the mortgage borrowed, P = The price of the house - The down payment

∴ P = $275,000 - 20/100 × $275,000 = $275,000 - $55,000 = $220,000

The principal of the mortgage, P = $220,000

The formula for the total amount paid which is the cost of the loan is given as follows;

\(Outstanding \ Loan \ Balance = \dfrac{P \cdot \left[\left(1+\dfrac{r}{12} \right)^n - \left(1+\dfrac{r}{12} \right)^m \right] }{1 - \left(1+\dfrac{r}{12} \right)^n }\)

The formula for monthly payment on a mortgage, 'M', is given as follows;

\(M = \dfrac{P \cdot \left(\dfrac{r}{12} \right) \cdot \left(1+\dfrac{r}{12} \right)^n }{\left(1+\dfrac{r}{12} \right)^n - 1}\)

A. When the mortgage term, t = 15-years,

The interest rate, r = 3%

The number of months over which the loan is payed, n = 12·t

∴ n = 12 months/year × 15 years = 180 months

n = 180 months

The monthly payment, 'M', is given as follows;

M =

The total amount paid over the loan term = Cost of the mortgage

Therefore, we have;

220,000*0.05/12*((1 + 0.05/12)^360/( (1 + 0.05/12)^(360) - 1)

\(M = \dfrac{220,000 \cdot \left(\dfrac{0.03}{12} \right) \cdot \left(1+\dfrac{0.03}{12} \right)^{180} }{\left(1+\dfrac{0.03}{12} \right)^{180} - 1} \approx 1,519.28\)

The minimum monthly payment for the loan, M ≈ $1,519.28

The total amount paid over loan term, A = n × M

∴ A ≈ 180 × $1,519.28 = $273,470

The total amount paid over loan term, A ≈ $270,470

B. When t = 20 year and r = 6%, we have;

n = 12 × 20 = 240

\(\therefore M = \dfrac{220,000 \cdot \left(\dfrac{0.06}{12} \right) \cdot \left(1+\dfrac{0.06}{12} \right)^{240} }{\left(1+\dfrac{0.06}{12} \right)^{240} - 1} \approx 1,576.15\)

The total amount paid over loan term, A = 240 × $1,576.15 ≈ $378.276

The monthly payment, M = $1,576.15

C. When t = 30 year and r = 5%, we have;

n = 12 × 30 = 360

\(\therefore M = \dfrac{220,000 \cdot \left(\dfrac{0.05}{12} \right) \cdot \left(1+\dfrac{0.05}{12} \right)^{360} }{\left(1+\dfrac{0.05}{12} \right)^{360} - 1} \approx 1,181.01\)

The total amount paid over loan term, A = 360 × $1,181.01 ≈ $425,163

The monthly payment, M ≈ $1,181.01

The mortgage to be chosen is the mortgage with the least total amount paid over the loan term so as to reduce the liability

Therefore;

The mortgage chosen is option A which is a 15-year mortgage term with a 3% interest rate;

The total amount paid over the loan term = $270,470

The sum of first 10 terms is 72.

Concept: Arithmetic Progression (AP) is a sequence of numbers in order, in which the difference between any two consecutive numbers is a constant value. It is also called Arithmetic Sequence.

Arithmetic Progression Formula

= an - a. nth term of an AP: an = a + (n - 1)d. Sum of n terms of an AP: Sn = n/2(2a+(n-1)d) = n/2(a + l), where l is the last term of the arithmetic progression.

Given:

Eighth term is 8.2

Common difference is 0.4

a(8) = 8.2

a + 7d = 8.2

Since d = 0.4

a + 7(0.4) =8.2

a = 5.4

Sum of 10 terms = n/2 (2a+(n-1)d)

= 5(2*5.4 + 9*0.4)

=5(10.8 +3.6)

Sum=72

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Answer: See the attached image.

I've rearranged the tiles in the proper order

===================================================

Explanation

For step 2, we rewrite each expression in terms of sines and/or cosines. For instance, tan = sin/cos.

In step 3, we focus on the stuff in the numerator only. So we focus on sin/cos+cos/sin. In this step, we multiply top and bottom of the first fraction by sine. We multiply top and bottom of the second fraction by cos. These steps are done to get the LCD.

In step 4, we are able to add the fractions because both fractions have the same denominator.

In step 5, we use the pythagorean trig identity sin^2+cos^2 = 1.

In step 6, we use the idea that (A/B) divide by (C/D) = (A/B)*(D/C).

The general solution to the ODE is: s(t) = a0 + a1t - a1t^3/6 - 5a1t^4/48 + a1t^5/120 + ...

To solve the non-linear ODE:

d²s/dt² + t² ds/dt = 0

We can use a power series method. We assume that the solution s(t) can be expressed as a power series in t:

s(t) = a0 + a1t + a2t^2 + ...

We then differentiate s(t) twice with respect to t:

ds/dt = a1 + 2a2t + 3a3t^2 + ...

d²s/dt² = 2a2 + 6a3t + 12a4t^2 + ...

Substituting these expressions into the ODE, we get:

2a2 + 6a3t + 12a4t² + ... + t² (a1 + 2a2t + 3a3t² + ...) = 0

Collecting terms with the same degree of t, we get:

t^0: 2a2 + a1 = 0

t^1: 6a3 + 2a2 = 0

t^2: 12a4 + 3a3 + a1 = 0

t^3: 20a5 + 4a3 = 0

t^4: 30a6 + 5a4 = 0

Solving for the coefficients, we get:

a2 = -a1/2

a3 = -a2/3 = a1/6

a4 = -a1/12 - 3a3/4 = -a1/12 - a1/8 = -5a1/24

a5 = -a3/2 = -a1/12

a6 = -a4/6 = a1/48

Therefore, the general solution to the ODE is:

s(t) = a0 + a1t - a1t^3/6 - 5a1t^4/48 + a1t^5/120 + ...

where a0 and a1 are constants determined by initial conditions.

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