Write the equation of a line that is perpendicular to y = 0.25x - 7 and that passes through the point (-6,8).

Answer:

x8 y6

Step-by-step explanation:

The solution to the IVP is:

\(y(x) = (43/20)e^{(6x)} - (27/20)e^{(-x)} - (63/20) + (47/20)e^{(x)]\)

The given differential equation is:

\(d^2y/dx^2 - 5dy/dx - 6y = 0\)

The auxiliary equation is:

\(r^2 - 5r - 6 = 0\)

This can be factored as:

(r - 6)(r + 1) = 0

So, the roots are r = 6 and r = -1.

The two fundamental solutions are:

\(y1(x) = e^{(6x)} and y2(x) = e^{(-x)}\)

To solve the initial value problem (IVP), we need to find the constants c1 and c2 such that the general solution satisfies the initial conditions:

y(0) = -7 and y'(0) = 7

The general solution is:

\(y(x) = c1e^{(6x)} + c2e^{(-x)}\)

Taking the derivative with respect to x, we get:

\(y'(x) = 6c1e^{(6x)}- c2e^{(-x)}\)

Using the initial condition y(0) = -7, we get:

c1 + c2 = -7

Using the initial condition y'(0) = 7, we get:

6c1 - c2 = 7

Solving these equations simultaneously, we get:

\(c1 = (43/20)e^{(-6x)} - (27/20)e^{(x)}\)

\(c2 = -(63/20)e^{(-6x)} + (47/20)e^{(x)}\)

Therefore, the solution to the IVP is:

\(y(x) = (43/20)e^{(6x)} - (27/20)e^{(-x)} - (63/20) + (47/20)e^{(x)]\)

Simplifying, we get:

\(y(x) = (43/20)e^(6x) + (7/20)e^{(-x)} - (63/20)\)

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Answer:

25x + 15y =18

Step-by-step explanation:

that is the answer cause x goes with shirts and y with mug and lastly 80 is the total

The number from greatest to least in the given set of numbers are:

-14/5 < -2.25 < 1 ¼ < 3/2

A group of numbers is referred to as an element and makes up a set of numbers. The collection of numbers in the set may be infinite or finite. Roster notation is a method for indicating sets. For example, the set "2,31" contains the elements 2 and 31.

We need a way to say which numbers are included when a set has an infinite number of elements because it is impossible to list them all. Our number system is based on a few well-known infinite sets.

Given mixed fractions and decimals:

-14/5, -2.25, 1 ¼, 3/2

So,

-14/5 = −2.8

-2.25

1 ¼ = 1.25

3/2 = 1.5

As, −2.8 < -2.25 < 1.25 < 1.5, The numbers from greatest to least are:

-14/5 < -2.25 < 1 ¼ < 3/2.

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Complete question:

By the concept of Semi-annually compounding In 2 half years the account will contain $100,000.

Semi-annually compounding interest means that the principal of a loan or investment, in this example every six months, at the start of the compounding period, includes the entire interest from each prior period. Theoretically, continuously compounded interest means that interest is continuously earned on an account balance as well as reinvested into the balance to increase future interest earnings. The amount of interest due on simple interest loans and investments is determined solely by the initial principle sum. When interest is compounded, the principle is increased by the sum of the interest from each prior month. You pay interest on interest when taking out loans with compound interest. You receive interest on the interest if your investment earns compound interest.

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Step-by-step explanation:

as the baseline of the abd triangle is a diameter of the circle (it goes through the center of the circle), c is the supplementary angle to 76° (it adds up to 180°), as c + 76 represents a half-circle.

c = 180 - 76 = 104°

the circle theorem says : the angle at the center is twice the angle at the circumference.

therefore a = 76/2 = 38°

similarly,

b = 104/2 = 52°

and remembering that the sum of all angles in a triangle is always 180°

d = 180 - 38 - 52 = 90°

which is true also, because all inscribed triangles in a half- circle with the baseline being the diameter, must be right-angled.

Answer:

1 solution

Step-by-step explanation:

4h + 2 = 3h - 7

Subtract 3h from both sides:

(4h + 2) - 3h = (3h - 7) - 3h

h + 2 = -7

Then, subtract 2 from both sides to isolate h:

(h + 2) - 2 = (-7) - 2

h = -9

There is one solution, -9.

The alternative hypothesis in this problem claims that the genuine population proportion of blue candies is less than 0.25, contrary to the null hypothesis, which states that the population proportion is 0.25.

At a significance level of 0.05, a proportions one-tailed z-test is employed to test this hypothesis. The test's critical value is -1.645, and the test statistic that was generated is -1.14. The estimated test statistic exceeds the crucial value, hence the null hypothesis is not rejected.

The candy company's assertion that the proportion of blue candies is 25% is therefore unsupported by sufficient proof. Hence, we cannot infer that the population's share of blue candies is different than 22%.

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Positive integers p and q ensure that p*q is always greater than 0.

A mathematical statement that has a "equal to" symbol between two expressions with equal values is called an equation. as in 3x + 5 Equals 15, for instance.

Equations come in a variety of forms, including linear, quadratic, cubic, and others.

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides.

We have LHS = RHS (left hand side = right hand side) in every mathematical equation. To determine the value of an unknown variable that represents an unknown quantity, equations can be solved. The statement is not an equation if there is no "equal to" sign in it.

Hence, Positive integers p and q ensure that p*q is always greater than 0.

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SAS postulate proves that this triangle is congruent.

Here is why,

Given that side GL = GK = LK;

which means that side GK of the triangle GKM is equal to the side KL of the triangle KLM , so one side become equal in both the triangles.

Now, KM is also the common side of the both the triangles so another side will become equal in both the triangles.

Lastly the angle KMG of the triangle KGM and the angle KML of the triangle KLM are the right angles in both the triangles and equal.

so, with 2 sides and one angle both the triangles become congruent to each other.

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The curl of the vector field

curl(F) = -2ey cos(z)i + 8ez cos(x)j - 9ex cos(y)k

The divergence of the vector field

div(F) = 9e^x sin(y) + 2e^y sin(z) + 8e^z

To find the curl of the vector field F(x, y, z) = 9ex sin(y), 2ey sin(z), 8ez sin(x), we need to compute the determinant of the curl matrix.

(a) Curl of F:

The curl of a vector field F = P(x, y, z)i + Q(x, y, z)j + R(x, y, z)k is given by the following formula:

curl(F) = (∂R/∂y - ∂Q/∂z)i + (∂P/∂z - ∂R/∂x)j + (∂Q/∂x - ∂P/∂y)k

In this case, we have:

P(x, y, z) = 9ex sin(y)

Q(x, y, z) = 2ey sin(z)

R(x, y, z) = 8ez sin(x)

Taking the partial derivatives, we get:

∂P/∂y = 9ex cos(y)

∂Q/∂z = 2ey cos(z)

∂R/∂x = 8ez cos(x)

∂R/∂y = 0 (no y-dependence in R)

∂Q/∂x = 0 (no x-dependence in Q)

∂P/∂z = 0 (no z-dependence in P)

Substituting these values into the curl formula, we have:

curl(F) = (0 - 2ey cos(z))i + (8ez cos(x) - 0)j + (0 - 9ex cos(y))k

= -2ey cos(z)i + 8ez cos(x)j - 9ex cos(y)k

Therefore, the curl of the vector field F is given by:

curl(F) = -2ey cos(z)i + 8ez cos(x)j - 9ex cos(y)k

(b) Divergence of F:

The divergence of a vector field F = P(x, y, z)i + Q(x, y, z)j + R(x, y, z)k is given by the following formula:

div(F) = ∂P/∂x + ∂Q/∂y + ∂R/∂z

In this case, we have:

∂P/∂x = 9e^x sin(y)

∂Q/∂y = 2e^y sin(z)

∂R/∂z = 8e^z

Substituting these values into the divergence formula, we have:

div(F) = 9e^x sin(y) + 2e^y sin(z) + 8e^z

Therefore, the divergence of the vector field F is given by:

div(F) = 9e^x sin(y) + 2e^y sin(z) + 8e^z

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Answer:

37

add all of them together then divide it by two

Answer:

c

Step-by-step explanation:

because 1 is also know as +1

The pH of the 0.100 M NH3 solution is approximately 11.13.

The pH of a solution is a measure of its acidity or alkalinity. In this case, we are asked to find the pH of a 0.100 M NH3 (ammonia) solution that undergoes dissociation. The dissociation equation for NH3 is NH3(aq) + H2O(l) → NH4+(aq) + OH-(aq).

To find the pH, we need to determine the concentration of the hydroxide ion (OH-) in the solution. Since the dissociation equation shows that NH3 reacts with water to form NH4+ and OH-, we can use the equilibrium constant, K1, to calculate the concentration of OH-.

The equilibrium constant expression for this reaction is K1 = [NH4+][OH-] / [NH3]. Since the initial concentration of NH3 is given as 0.100 M, and the equilibrium concentration of NH4+ is equal to the concentration of OH-, we can rewrite the equation as K1 = [OH-]2 / 0.100.

Given that the value of K1 is 1.8 x 10^5, we can solve for [OH-]. Rearranging the equation, we have [OH-]2 = K1 x [NH3]. Plugging in the values, [OH-]2 = (1.8 x 10^5)(0.100), which simplifies to [OH-]2 = 1.8 x 10^4.

Taking the square root of both sides, we find [OH-] = √(1.8 x 10^4). Evaluating this, we get [OH-] ≈ 134.16.

Now, we can calculate the pOH of the solution using the formula pOH = -log[OH-]. Substituting in the value of [OH-], we have pOH = -log(134.16), which gives us a pOH of approximately 2.87.

Finally, we can calculate the pH of the solution using the relationship pH + pOH = 14. Rearranging the equation, we find pH = 14 - pOH. Plugging in the value of pOH, we have pH ≈ 14 - 2.87 = 11.13.

Therefore, the pH of the 0.100 M NH3 solution is approximately 11.13.

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a. H₀ (Null hypothesis) =0 and H₁ Alternative hypothesis is 0.

b. Degrees of freedom is 102.

b. Test statistic: t = 2.161

c. Critical values at 0.10 level of significance: t-critical_1= -1.984, t-critical_2 ≈ 1.984

e. There is a significant linear relationship between the score on the standardized test and the first-year college grade point average based on the sample results

(a) The null hypothesis (H₀) states that there is no significant linear relationship between the score on the standardized test and the first-year college grade point average.

The alternative hypothesis (H₁) states that there is a significant linear relationship between the two variables.

H₀: ρ = 0 (population correlation coefficient is zero)

H₁: ρ ≠ 0 (population correlation coefficient is not zero)

(b) The appropriate test statistic to use in this case is the t-statistic.

Degrees of freedom: df = n - 2

= 104 - 2

= 102

(c) To find the value of the test statistic, we need to calculate the t-value using the sample correlation coefficient (r) and the degrees of freedom (df).

t = r × √((df) / (1 - r²))

Plugging in the values: r = 0.22 and df = 102,

t = 0.22× √(102 / (1 - 0.22²))

t=2.161

(d) To find the two critical values at the 0.10 level of significance:

Since it's a two-tailed test and the significance level is 0.10, we divide it by 2 to get 0.05 for each tail.

Using a t-distribution table or statistical software with df = 102, we find the critical t-values for a cumulative probability of 0.05 in each tail:

t-critical_1 =  -1.984

t-critical_2 = 1.984

(e)  Comparing the test statistic (|t|) to the critical values:

|t| = |2.161| = 2.161

Since |t| = 2.161 > t-critical_1 = -1.984 and

|t| = 2.161 > t-critical_2 = 1.984

we can conclude that there is a significant linear relationship between the score on the standardized test and the first-year college grade point average at the 0.10 level of significance.

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Answer:

14

Explanation:

To evaluate the expression, we need to replace x by 4. So, the expression is equal to:

3x + 2

3(4) + 2

12 + 2

14

Therefore, the value of the expression is 14

A principal gathered data about the distance in miles that his teachers and bus drivers live from the school. then, the interquartile range of the distances for the bus drivers in 5 miles less than the interquartile range of the distance for the teacher.

Interquartile Range:

In descriptive statistics, the interquartile range (IQR) is a measure of the statistical distribution, the distribution of data. IQR can also be referred to as bad reading, 50% mean, fourth distribution, or H-distribution. It is defined as the difference between the 75th and 25th percentile of the data. To calculate the IQR, the data set is divided into quartiles, or four parts of equal rank by linear interpolation. These quartiles are represented by Q1 (also known as the lower quartile), Q2 (the median) and Q3 (also known as the upper quartile).

The lower quartile is the 25th percentile and the upper quartile is the 75th percentile, so IQR = Q3 − Q1

Basically, the interquartile range represents the width or “spread” of the collection. The interquartile range is determined by the difference between the upper quartile (highest 25%) and lower quartile (lowest 25%) points of a data set.

From the figure, we can find:

The interquartile range of the bus driver is: 20 -10 = 10

The interquartile range of the teacher is: 30 -15 = 15

Therefore,

the interval interquartile distance is bus The driver's distance was 5 miles less than the interquartile range of the teacher's distance.

Complete Question:

A principal gathered data about the distance in miles that his teachers and bus drivers live from the school .The box plots below show these data.

(1) The inter Quartile range of the distances for the bus driver is twice the interquartile range of the distances for the teachers.

(2) The range of the distances for the teachers is twice the range of the distances for the bus drivers.

(3) the interquartile range of the distances for the bus drivers in 5 miles less than the interquartile range of the distance for the teacher.

(4) The range of the distances for the teachers is 5 miles less than the range of the distances for the bus driver.

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Answer: C. The interquartile range of the distances for the bus drivers is 5 miles less than the interquartile range of the distances for the teachers.

Answer:  430000

Step-by-step explanation: you have to do pemdas

Answer: 430,000. /four hundred thirty thousand

Step-by-step explanation:

The value of 4.3 x 10^5 is 430,000.

To understand this, the notation 4.3 x 10^5 represents a number in scientific notation, where 4.3 is the coefficient or significand, and 10^5 is the exponent. The exponent of 10 tells us how many places to move the decimal point to the right. In this case, the exponent 5 means we need to move the decimal point five places to the right.

Starting with 4.3, we move the decimal point five places to the right to get 430,000. So, 4.3 x 10^5 is equivalent to 430,000.

Answer: 3 or 4

Step-by-step explanation:

For the three red lights, we have a "9 sockets choose 3" option. In those 9C3 methods. The solution is 1260 (9C3) (6C4)(2C2).

For the three red lights, we have a "9 sockets choose 3" option. In those 9C3 methods.

There are now just 6 open sockets after the 3 red bulbs have been installed.

Put three red bulbs in the first three sockets.

None = 9C3

There are 4 yellow bulbs in 4 sockets.

Way count is 6C4

Two sockets hold two blue bulbs.

Number of ways = 2C2

For the four yellow lights, we have a choice of "6 sockets, choose 4" 6C4 in that manner.

There are just 2 open sockets left once the 4 red lights are screwed in.

The blue lights are available in "2 sockets pick 2." Consequently, (2C2) = 1 way.

Once those two bulbs were screwed in, a bulb was present in each socket.

Total number of methods is 84 * 15 * 1 or 9C3 * 6C4 * 2C2.

1260 different ways in total.

So, there are 1260 total ways.

The solution is 1260 (9C3) (6C4)(2C2).

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Answer: The equation a+b+c=240 degrees is not true for any triangle, since the sum of the angles of a triangle is always 180 degrees. However, it could be true for a quadrilateral, which has four angles. One way to explain why a+b+c=240 degrees is to use the fact that opposite angles of a cyclic quadrilateral (a quadrilateral that can be inscribed in a circle) are supplementary, meaning they add up to 180 degrees. If we label the opposite angle of c as d, then we have c+d=180 degrees. Subtracting c from both sides, we get d=180-c. Then, adding a+b to both sides, we get a+b+d=240-c+c, which simplifies to a+b+c=240 degrees. Another way to explain why a+b+c=240 degrees is to use the fact that an exterior angle of a triangle is equal to the sum of the opposite interior angles. If we extend one side of the triangle and label the exterior angle as e, then we have e=a+b. Then, adding c to both sides, we get e+c=a+b+c. Since e+c is an exterior angle of another triangle formed by extending the side, it is equal to 180 degrees. Therefore, we have 180=a+b+c, which implies that a+b+c=240 degrees.

Answer:

m∠JKM = 63°

m∠MKL = 27°

Step-by-step explanation:

Since ∠JKL is a right angle. This means that by summing up both m∠JKM and m∠MKL will result in the same as ∠JKL figure. Thus, m∠JKM + m∠MKL = m∠JKL which is 90° by a right angle definition.

\(\displaystyle{\left(12x+3\right)+\left(6x-3\right) = 90}\)

Solve the equation for x:

\(\displaystyle{12x+3+6x-3 = 90}\\\\\displaystyle{18x=90}\\\\\displaystyle{x=5}\)

We know that x = 5. Next, we are going to substitute x = 5 in m∠JKM and m∠MKL. Thus,

m∠JKM = 12(5) + 3 = 60 - 3 = 63°

m∠MKL = 6(5) - 3 = 30 - 3 = 27°

Answer:

are or rectangle = l*b

252= (x+2) (2x+1)

252= 2x²+x+ 4x +2

2x²+5x -250=0

(x-10) (2x+25)=0

so x=10

using sum and product method

Step-by-step explanation:

Answer:

20

Step-by-step explanation:

5(x-1)

Replace x with its value.

5(5-1)

Solve parenthesis first.

5(4)

Multiply.( multiply 5 times 4)

20

The average rate of change per hour in the temperature is 0.83 degrees.

To find the average rate of change per hour, we need to divide the total change in temperature by the number of hours over which the temperature changed.

The temperature rose by 5 degrees from 6:00 am to 12:00 pm, which is a period of 6 hours.

Therefore, the average rate of change per hour can be calculated as follows:

average rate of change per hour = total change in temperature / number of hours

So, we have

average rate of change per hour = 5 degrees / 6 hours

average rate of change per hour = 0.83 degrees/hour (rounded to two decimal places)

So, the average rate of change per hour is 0.83 degrees.

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Answer:

In terms of algebra, the point (1, -5) fulfills the first inequality, but not the second, since -5 is not bigger than -5. The point (1, -5) on the graph is in the shaded region of the first inequality, but it is on the dashed line of the second inequality, which is not inclusive.

The system of inequalities are solved and the solution is not ( 1 , -5 )

Inequalities are the mathematical expressions in which both sides are not equal. In inequality, unlike in equations, we compare two values. The equal sign in between is replaced by less than (or less than or equal to), greater than (or greater than or equal to), or not equal to sign.

In an inequality, the two expressions are not necessarily equal which is indicated by the symbols: >, <, ≤ or ≥.

Given data ,

Let the inequality equation be represented as A

Now , the value of A is

Substituting the values in the equation , we get

y ≤ 3x + 2   be equation (1)

y > -2x - 3   be equation (2)

Now , on simplifying , we get

when x = 1 and y = -5

-5 ≤ 3 ( 1 ) + 2

-5 ≤ 5

Therefore , the inequality is true

And , when x = 1 and y = -5

-5 > -2 ( 1 ) - 3

-5 > -5

The inequality is false

Therefore , we can see that the point (1, -5) falls within the shaded region of the first inequality (below the line) but outside the shaded region of the second inequality (above the line).

Hence , the point satisfies the first inequality but not the second inequality

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Answer:

Step-by-step explanation:

Don't be too quick to answer 15% of some number. It may be right, but it is likely not.

James makes 9.00 dollars an hour

Priya makes 20% more than James. Stop. Figure that out.

9.00 * 1  + 25/100 * 9 = 9.00 + 2.25 = 11.25

Now, you can figure out 5% less.

Siobhan = 11,25 - 5/100 * 11.25

Siobhan = 11.25 - 0.05 * 11.25

Siobhan = 11.25 - 0.5625

Siobhan = 10.6875 = 10.69

There is no other way that I know of to go directly to Siobhan's wage other than doing it the long way -- at least for the level of math you are taking.

9 * (1.2 - 0.05) might work.

9 * (1.15)

= 10.35 which is close, but not correct.  

Moral: do the math. Don't accept a guess as an answer.

Answer:

75%

Step-by-step explanation:

You take the length of the lower arm, 21, and divide it by the total length, 28. Your equation should be 21/28 = 3/4 =.75. 0.75 is equal to 75%

Answer:

75%

Step-by-step explanation:

You take the length of the lower arm, 21, and divide it by the total length, 28. Your equation should be 21/28 = 3/4 =.75. 0.75 is equal to 75%

The cat ran 3 miles in one hour

A car runs 3/5 of a mile in 2/10

The number of miles ran in one hour can be calculated as follows

3/5= 2/10

x= 1

Cross multiply

2/10x= 3/5

x= 3/5 ÷ 2/10

= 3/5 × 10/2

= 3

Hence the car ran 3 miles in 1 hour

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