find the roots of the quadratic equation :
\(x ^{2} + x + 2 = 0\)
No copied ans no spams​

Answer:

Step-by-step explanation:

4x + 20 + 2x =90 degree (being perpendicular)

6x + 20=90

6x =90-20

6x =70

x=70/6

x=11.66666667

well, if he sold 10 for $25, let's see how much he sold all 12 for.

\(\begin{array}{ccll} eggs&\$\\ \cline{1-2} 10 & 25\\ 12& x \end{array} \implies \cfrac{10}{12}~~=~~\cfrac{25}{x} \\\\\\ \cfrac{5}{6} ~~=~~ \cfrac{25}{x}\implies 5x=150\implies x=\cfrac{150}{5}\implies x=30\)

so he sold all 12 for $30, whilst he bought them for $25, so he had $5 profit, now, if we take 25(origin amount) as the 100%, what's 5 off of it in percentage?

\(\begin{array}{ccll} Amount&\%\\ \cline{1-2} 25 & 100\\ 5& y \end{array} \implies \cfrac{25}{5}~~=~~\cfrac{100}{y} \\\\\\ 5 ~~=~~ \cfrac{100}{y}\implies 5y=100\implies y=\cfrac{100}{5}\implies y=\stackrel{ \% }{20}\)

Step-by-step explanation:

It looks like you have provided the recursive formula for a sequence, with the initial condition of A(1) = 5/3.

To find the values of the sequence, we can use the recursion formula, which tells us that each term in the sequence is equal to the previous term multiplied by x-9. We can start by finding A(2), which will be:

A(2) = A(1) x (x-9)

A(2) = (5/3) x (x-9)

We can continue this process to find the next terms in the sequence. We can express A(3) in terms of A(2), and then A(4) in terms of A(3), and so on. Here is the general expression for A(n):

A(n) = (5/3) x (x-9)^{n-1}

So, given any value of x, we can use this formula to find the nth term in the sequence.

For example, if x=2, we can find the first few terms of the sequence:

A(1) = 5/3

A(2) = (5/3) x (2-9) = -15

A(3) = (5/3) x (2-9)^2 = 135/4

A(4) = (5/3) x (2-9)^3 = -6075/8

And so on.

Answer:

Step-by-step explanation:

The integral of (42³ - 2r + 7) dz is equal to (42³ - 2r + 7)z + C.

To integrate the function (42³ - 2r + 7) dz, we treat r as a constant and integrate with respect to z. The integral of a constant with respect to z is simply the constant multiplied by z:

∫ (42³ - 2r + 7) dz = (42³ - 2r + 7)z + C

where C is the constant of integration.

Note: The integral of a constant term (such as 7) with respect to any variable is simply the constant multiplied by the variable. In this case, the variable is z.

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Answer:

Option A that is best describes the given scenario is option A that is “LaTricia is not correct. The word product does mean to multiply, but 12 should be the product and 3 should be one of the factors.”

Step-by-step explanation:

Given that LaTricia wrote a sentence as an equation.  Given sentence is “Twelve is the product of three and a number”

Expression written by LaTricia =

Lets first concentrate on sentence and we will create our expression based on sentence and check it against the expression created by LaTricia.  Let the number represented by variable w.

So product of 3 and the number will be represented by

And as Twelve is the product of three and a number

That is three is one of the factor and result product is 12. Hence option A that is best describes the given scenario is option A that is “LaTricia is not correct. The word product does mean to multiply, but 12 should be the product and 3 should be one of the factors.”

Answer:

The image I put is the answer.

Step-by-step explanation:

The estimate of the mean number of hours worked by all university students within a 90% confidence interval is (21.25 hours, 24.75 hours). The error window is 1.25 hours.

We can use the formula below to determine the estimate with a 90% confidence interval:

Margin of error + sample mean equals Confidence Interval.

Information disclosed:

Student sample size (n): 64

Mean sample: 23 hours

5 hours is the population standard deviation.

Level of confidence: 90%

Let's begin by computing the margin of error using the following formula:

The margin of error is calculated as Critical Value * (Standard Deviation / Sample Size).

We may utilise the Z-distribution to get the crucial value since we are aware of the population standard deviation. The essential value for a 90% degree of confidence is 1.645 (found in the Z-table).

Margin of Error = 1.645 * (5 / 64) = 1.645 * (5 / 8), etc. Margin of Error = 1.645 * 0.625, etc.

As a result, the error window is roughly 1.03 hours.

Next, we may determine the confidence interval's lower and upper bounds:

Lower Bound is equal to Sample Mean - Margin of Error, or 23 - 1.03 = 21.97.

Upper Bound is equal to Sample Mean plus Margin of Error, which is 23 + 1.03 = 24.03.

The estimate for the mean number of hours worked by all university students within a 90% confidence interval is thus (21.97 hours, 24.03 hours). There is a 1.03 hour inaccuracy in the calculation.

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To set up the double integral for calculating the flux of the vector field \(F⃗ (x,y,z)=xi⃗ +yj⃗ t\). The final answer is the flux of \(F⃗\) through the open-ended circular cylinder is \(288π.\)

Through the open-ended circular cylinder of radius 8 and height 9 with its base on the xy-plane and centered about the positive z-axis, we need to use the divergence theorem.

Let S be the surface of the cylinder and V be the region enclosed by the surface. The divergence theorem states that the flux of \(F⃗\) through S is equal to the triple integral of the divergence of \(F⃗\)over V.

\(div(F⃗ )\)= \(∂Fx/∂x + ∂Fy/∂y + ∂Fz/∂z\) \(= 1 + 1 + 0 = 2\)

Therefore, the flux of \(F⃗\) through S is given by the triple integral of 2 over V, which can be written as a double integral over the cross-sectional area of the cylinder at a fixed z-value:

\(Φ = ∬S F⃗ · dS = ∬D F⃗ · n⃗ dS = ∫ ∬D (F⃗ · k⃗ ) dA\)

where D is the circle of radius 8 in the xy-plane centered at the origin, \(k⃗\)is the unit vector in the z-direction, and dA is the area element in the xy-plane. To evaluate the double integral, we can use cylindrical coordinates (r, θ, z):\(Φ = ∫0^9 ∫0^8 2r dz dr dθ\)

The limits of integration for z and r come from the height and radius of the cylinder, while θ ranges from 0 to 2π because of the circular symmetry.

Simplifying the double integral, we get:

Φ = 2 ∫\(0^9\) ∫\(0^8\) r dz dr dθ

= 2 ∫\(0^9\) \(8r\) dθ

= \(2(8)(9)(2\pi )\)

= 288π

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Answer:

The y Coordinates

Step-by-step explanation:

when running a line, in a right-triangle, from the 90° angle perpendicular to its opposite side, we will end up with three similar triangles, one Small, one Medium and a containing Large one.  Check the picture below.

\(\cfrac{24}{y}=\cfrac{y}{30}\implies 720=y^2\implies \sqrt{720}=y\implies 12\sqrt{5}=y\implies 26.83\approx y\)

Answer:

x=28.75

Step-by-step explanation:

Pythagoras' theorem is named after Pythagoras, who was a Greek mathematician that lived around 500 B.C. It is a geometric principle that states that in a right-angled triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides (the legs). This can be represented by the equation a² + b² = c², where c is the hypotenuse and a and b are the lengths of the other two sides.

The proof of the Pythagorean Theorem can be done in various ways. One common method involves drawing squares on each side of a right-angled triangle and comparing their areas. Another method involves using similar triangles and the concept of ratios.

The Pythagorean Theorem has also been extended to apply to three-dimensional objects, such as pyramids and spheres. In these cases, the theorem relates to the surface areas and volumes of the objects.

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Answer:

A. KEJ and E. JKE

Step-by-step explanation:

Triangles can be named by their points in any order, the points on this triangle are K, J, and E. These can rearranged in any order to name the triangle.

hope this helps!

Stephen's average speed for the round trip was 48 mph.

To find Stephen's average speed, we can use the formula:

Average Speed = Total Distance / Total Time

Let's assume the distance from Stephen's house to his aunt's house is 'd' miles.

On the way to his aunt's house, Stephen traveled at a speed of 60 mph. So the time taken for this leg of the trip is given by:

Time = Distance / Speed = d / 60

On the return trip, Stephen traveled at a speed of 40 mph. So the time taken for this leg of the trip is:

Time = Distance / Speed = d / 40

The total time for the round trip is the sum of the times for the outward and return trips:

Total Time = d / 60 + d / 40

To find the average speed, we divide the total distance by the total time:

Average Speed = Total Distance / Total Time

The total distance for the round trip is 2d (since it's the same roadway for both trips).

Average Speed = 2d / (d / 60 + d / 40)

Simplifying this expression, we get:

Average Speed = 2d / ((3d + 2d) / 120) = 2d / (5d / 120) = 2d * 120 / 5d = 240 / 5 = 48 mph

Therefore, Stephen's average speed for the round trip was 48 mph.

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Answer:

67.20$

Step-by-step explanation:

multiply 56 by 1.2

Answer:

$67.2

Step-by-step explanation:

Given:

∴ Equation: Price + Tip = Total

Simplify the equation to obtain the total:

Convert the expression in the parenthesis into decimals:

Open the parenthesis and simplify:

Faith will pay (including the tip) $67.2.

Answer:

\((2^3)^2 = 64\)

Step-by-step explanation:

Option 1:

Using the following rule:

\((a^n)^m = a^{nm}\)

Put in our expression,

a = 2

n = 3

m = 2

\((a^n)^m = a^{nm}\)

\((2^3)^2 = 2^{3*2}=2^6=64\)

Option 2:

Using the following rule:

\(a^n * a^m = a^{n+m}\)

Since our expression is the same as multiplying 2³ with itself, we can write it as a multiplication.

\((2^3)^2 = 2^3 * 2^3\)

If we compare this with \(a^n * a^m\), we can see that

a = 2

n = 3

m = 3 (in this case, n and m are equal)

\(a^n*a^m = a^{n+m}\)

\(2^3*2^3 = 2^{3+3} = 2^6 = 64\)

Answer: \((2^3)^2 = 64\)

Answer:

Formula used : (a^m)^n = a^(m×n)

→ (2³)² = 2³*² = 2⁶ = 64

Answer:

V ≈ 3367.6 cm³

Step-by-step explanation:

The volume (V) of a sphere is calculated as

V = \(\frac{4}{3}\) πr³ ( r is the radius )

Here D = 18.6 , then r = 18.6 ÷ 2 = 9.3 , so

V = \(\frac{4}{3}\) × 3.14 × 9.3³

   = \(\frac{4}{3}\) × 3.14 × 804.357

   = \(\frac{4(3.14)(804.357)}{3}\)

   ≈ 3367.6 cm³ ( to the nearest tenth )

Answer:

--------------------------

Hope it helps...

Answer:

(A) Over the interval [-2.5, 0.5], the local maximum is 2.

Step-by-step explanation:

"Over the interval [-2.5, 0.5], the local maximum is 2."

Correct. The local maximum is the maximum, or highest point, of the graph in a certain area of interval. In [-2.5, 0.5], the highest point is at the y-value of 2.

"As the x-values go to positive infinity, the function's values go to negative infinity."

Wrong. As the x values go to positive infinity (meaning they go to the right, or positive side of the graph), the function goes up, meaning the function's values go to positive infinity.

"The function is decreasing over the interval (-1, 0.75)."

Wrong. Only from [-1, 0] is where that area of the graph decreases. The other half of it, (0, 0.75), is where the graph increases.

"The function is negative for the interval [-2, 0]."

Wrong. Only from [-1, 0] is the function negative. In the interval [-2, -1], the function is positive.

Hope that helps (●'◡'●)

9514 1404 393

Answer:

  275

Step-by-step explanation:

Let h represent the number of hamburgers sold. Then the number of cheeseburgers sold is h-62, and the combined total is ...

  hamburgers + cheeseburgers = combined total

  h + (h -62) = 488

  2h = 550 . . . . . . . . add 62, collect terms

  h = 275 . . . . . . . . . .divide by 2

275 hamburgers were sold on Friday.

Answer:

£616

Step-by-step explanation:

700 - 12% = 616

616 is 12% less than 700

Answer:

Step-by-step explanation:

Recursive formula

a1 = -17

a^n = a^n-1 + 5

Explicit formula:

a^n = -17 + (n-1) * 5

The bank loaned out at an rate $15,000.00 at 8% annual interest and $11,000.00 at 14% annual interest.

Let the part of the money loaned at 8% be x.Then the part loaned at 14% is 26000 - x.Annual interest earned on x at 8% = 0.08x.Annual interest earned on (26000 - x) at 14% = 0.14(26000 - x)The sum of both interests = $2,740.00. Therefore:0.08x + 0.14(26000 - x) = 2,740.00Simplify and solve for x.0.08x + 3640 - 0.14x = 2,740.00-0.06x + 3640 = 2,740.00-0.06x = -900.00x = 15,000.00Hence, the bank loaned out at an rate $15,000.00 at 8% annual interest and $11,000.00 at 14% annual interest.

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Answer:

           \(\bold{-}\frac{\boxed{\bold{11}}}{\boxed{\bold{4}}}\)

Step-by-step explanation:

In arithmetic sequence the terms increase by the same number (d).

So d is the difference between any pair of next and previous term.

\(d=-\frac14-1=-1\frac14=-\frac54\)

Therefore the next term will be:

\(-\frac32+d=-\frac32+(-\frac54)=-\frac64-\frac54=-\frac{11}4\)

Answer:

Step-by-step explanation:

x-.20x

Lets say the hat cost $100

x=100

multiplying 100 by 20% which is .20 yields $20

S0 $20 is the discount which we subtract from the original price

100-20 and get the sale price of $80

They use a shortcut so you don't have to do the subtracting of the discount

They say if the price is being discounted subtract the discount from 1 and multiply that by the original amount

So in this case the discount percent was 20% = .20

Subtracted from 1

1-.20=.80

Since x is the original price we multiply x by the .80 to get  

.80x

Answer: 24 3/25

Step-by-step explanation:

Divide 600 by 25, giving you 24. The rest goes into the fraction part.

Trả lời:

86 và 91

Giải thích từng bước:

Cho hai số là x và y. Nếu tổng của chúng là 177, thì;

x + y = 177 ... 1

Nếu 17 bị trừ đi số đầu tiên, nó được biểu thị là x - 17

Nếu 25 được thêm vào số thứ hai l, nó được biểu thị bằng y + 25

Nếu số thứ nhất bây giờ bằng 2/3 số thứ hai, thì:

x-17 = 2/3 (y + 25) .... 2

Từ 1, x = 177-y ... 3

Thay thế 3 thành 2

177-y-17 = 2/3 (y + 25)

160-y = 2/3 (y + 25)

3 (160-y) = 2 (y + 25)

480-3y = 2y + 50

-3y-2y = 50-480

-5y = -430

y = 430/5

y = 86

Vì x = 177-y

x = 177-86

x = 91

Do đó hai số là 86 và 91

Answer:

62p+24

Step-by-step explanation:

1. you start with distributive property

p(-2)+4(-2)+8p(8)+4(8)

2. multiply

-2p-8+64p+32

3. Add the like terms

-2p+64p-8+32

4. Add

62p+24

a) The Pearson correlation coefficient is 0.76.

b) Null hypothesis: There is no significant correlation between the grades in English and Mathematics (H0: r = 0)

Alternative hypothesis: There is a significant correlation between the grades in English and Mathematics (Ha: r ≠ 0)

c) The regression line is: y = 0.64x + 34.18

d) Interpretation and conclusion:  The Pearson correlation coefficient (r) of 0.76 indicates a strong positive correlation between the grades in English and Mathematics.

Correlation analysis:

Using the Pearson correlation coefficient to measure the strength and direction of the linear relationship between two variables.

Hypothesis testing:

Setting up null and alternative hypotheses, and using the t-test to determine whether the correlation coefficient is statistically significant.

Linear regression:

Finding the equation of the regression line that best describes the relationship between the two variables.

Interpretation and conclusion:

Using the results of the analysis to draw meaningful conclusions about the relationship between the two variables and the sample population as a whole.

Here we have

A study was conducted to determine the relationship existing between the grade in English and the grade in mathematics. a random sample of 10 students in uc was taken and the following are the results of the sampling

Student           1     2      3     4     5     6     7     8      9    10

English          75   83   80   77   89   78   92   86   93   84

Mathematics 78   87   78   76   92   81    89   89   91   84​  

a) To compute the Pearson correlation coefficient (r), first calculate the mean, standard deviation, and covariance of the two variables:

Mean of English grades (x)

= (75+83+80+77+89+78+92+86+93+84)/10 = 83.7

Mean of Math grades (y)

= (78+87+78+76+92+81+89+89+91+84)/10 = 84.5

The standard deviation of English grades (Sx)

= √((75-83.4)²+(83-83.4)²+...+(84-83.4)²)/9) = 6.52

The standard deviation of Math grades (Sy)

= √((78-84.4)²+(87-84.4)²+...+(84-84.4)²)/9) = 5.47

Covariance of the two variables

= ((75-83.4)(78-84.4)+(83-83.4)(87-84.4)+...+(84-83.4)(84-84.4))/9 = 26.6

Using the formula, r = cov(X,Y)/(SxSy),

we can calculate the correlation coefficient as follows

r = 26.6/(6.52*5.47) = 0.76

Therefore,

The Pearson correlation coefficient is 0.76.

b) Null hypothesis: There is no significant correlation between the grades in English and Mathematics (H0: r = 0)

Alternative hypothesis: There is a significant correlation between the grades in English and Mathematics (Ha: r ≠ 0)

c) To find the equation of the regression line, we need to calculate the slope (b) and the intercept (a) of the line. The formula for the slope is:

b = r(Sy/Sx) = 0.76(5.47/6.52) = 0.64

The formula for the intercept is:

=> a = y - bx = 84.4 - 0.64(83.4) = 34.18

Therefore,

The equation of the regression line is:

y = 0.64x + 34.18

Interpretation and conclusion:

The Pearson correlation coefficient (r) of 0.76 indicates a strong positive correlation between the grades in English and Mathematics.

The p-value associated with this correlation coefficient can be used to test the null hypothesis.

The equation of the regression line shows that for every one-point increase in the English grade, the predicted increase in the Mathematics grade is 0.64 points.

Therefore,

a) The Pearson correlation coefficient is 0.76.

b) Null hypothesis: There is no significant correlation between the grades in English and Mathematics (H0: r = 0)

Alternative hypothesis: There is a significant correlation between the grades in English and Mathematics (Ha: r ≠ 0)

c) The regression line is: y = 0.64x + 34.18

d) Interpretation and conclusion:  The Pearson correlation coefficient (r) of 0.76 indicates a strong positive correlation between the grades in English and Mathematics.

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