Which expression is equivalent to 12x + 36y

Answer:

37°, 39° and 104°.

Step-by-step explanation:

In a triangle, all the 3 angles sum up to 180°.

3a + 8a + 37 = 180

11a = 180 - 37

11a = 143

a = 13

Angle 1 = 37

Angle 2 = 3a

= 3 × 13

= 39°

Angle 3 = 8a

= 8 × 13

= 104°

So, the angles are 37°, 39° and 104°.

Hope this helps!

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If y = xy + x² + 1, then when x=-1,

dy/dx = -1/2

The rate of change of a function with respect to a variable are called Derivatives.

Given that, y = xy + x² + 1

Put x = -1 we get,

y = -1y + (-1)² + 1

y = -y + 1 + 1

y = 1

Now Differentiating the given equation w.r.t x

dy/dx = xdy/dx + y + 2x

dy/dx - xdy/dx = y + 2x

dy/dx (1 - x) = y + 2x

dy/dx = (y + 2x)/(1 - x)

Put x = -1 and y = 1 we get

dy/dx = (1 + 2(-1))/(1 - (-1))

dy/dx = -1/2

Hence, y = xy + x² + 1, then when x=-1,

dy/dx = -1/2

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Answer: Continuous variables

A variable is said to be continuous if it can assume an infinite number of real values within a given interval

Step-by-step explanation: yep

Answer:

\(\boxed{\sf n= \dfrac{2}{5} ,\: n=1}\)

Step-by-step explanation:

\(\rightarrow 5n^2 = 7n -2\)

\(\rightarrow 5n^2 - 7n +2=0\)

\(\rightarrow 5n^2 - 5n -2n+2=0\)

\(\rightarrow 5n(n - 1) -2(n-1)=0\)

\(\rightarrow (5n-2)(n-1)=0\)

\(\rightarrow 5n-2= 0,\: n-1=0\)

\(\rightarrow 5n= 2,\: n=1\)

\(\rightarrow n= \dfrac{2}{5} ,\: n=1\)

Step-by-step explanation:

\(\hookrightarrow\sf{5n^2 = 7n -2}\\\\\hookrightarrow\sf{5n^2 - 7n +2=0}\\\\\hookrightarrow\sf{5n^2 - (5+2)n +2=0}\\\\\hookrightarrow\sf{5n^2 - 5n -2n+2=0}\\\\\hookrightarrow\sf{ 5n(n - 1) -2(n-1)=0}\\\\\hookrightarrow\sf{ (5n-2)(n-1)=0}\\\\\hookrightarrow\sf{ 5n-2= 0\:or~ n-1=0}\\\\\hookrightarrow\sf{ 5n= 2\:or~n=1}\\\\\hookrightarrow\bold{ n= \dfrac{2}{5} \:or~ n=1}\)

Answer:

The correct option is The PLUS loan will have a higher balance by $34.10 at the time of repayment. Hence Option B is correct.

Step-by-step explanation:

Answer:

Upper Right

Step-by-step explanation:

All of them have different dips, therefore the one facing in a different direction must be the odd one out.

Answer:

top right graph

Step-by-step explanation:

3 of the 4 graphs start at negative infinity for negative x, and approach infinity as x approaches infinity.

The top right graph starts at infinity for negative x and approaches negative infinity as x approaches infinity.

Answer: top right graph

The shortcut method of dividing a polynomial by a linear polynomial by using only the coefficients of the terms of the polynomial is called synthetic division.

Synthetic division is a simplified method of dividing a polynomial by a linear polynomial. It is used to divide a polynomial by a linear polynomial that is of the form x-c, where c is a constant. The synthetic division method is based on dividing the polynomial by the linear polynomial by using the coefficients of the terms of the polynomial.

The quotient and the remainder of the division are obtained by performing a few simple arithmetic operations. It is a quick and efficient way to divide polynomials and is particularly useful when dividing polynomials with large degrees

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Given the function h(x) = x² - 7x - 8. The extremum of the function is the minimum one and its value is h(x) = -32.5

The relation between symmetry of the graph and the extremum point is:

Suppose x = p is the line equation of the graph's symmetry, then f(p) is the extremum value.

The given function is:

h(x) = x² - 7x - 8

Find the x-intercepts:

h(x) = 0

x² - 7x - 8 = 0

(x + 1) (x - 8) = 0

x = -1 or x = 8

The symmetry lies in the middle of x-intercepts. Hence, the symmetry occurs at:

x = (-1 + 8) / 2

x = 3.5

The extremum point is:

h(3.5) = 3.5² - 7 x 3.5 - 8 = -32.5

Since the quadratic term x²  has a positive coefficient, the graph is open downward, hence the extremum point is the minimum one.

Complete question:

Find the extremum of each function using the symmetry of its graph. classify the extremum of the function as a maximum or a minimum and state the value of x at which it occurs. h(x) = x² - 7x - 8

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Answer:

14200

Step-by-step explanation:

The formula of amount be , A = P + SI = P + {(P × R × T)/100} = 14200

Simple interest exists estimated with the following formula:

S.I. = (P × R × T)/100,

where P = Principal, R = Rate of Interest in % per annum, and T = Time, usually computed as the number of years.

The rate of interest is in percentage r% and exists to be noted as r/100.

Given: P = 6000, T = 10 and R = 12

S.I. = (P × R × T)/100

\($SI = (6000*12*10)/100\)

SI = 7200

A = P + SI

A = 6000 + 7200

A = 14200

Therefore, the amount = 14200.

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Answer: Non proportional

Step-by-step explanation:

To know if the values given are proportional or not, we will use the formula:

y = kx

where

y = number of organisms

x = number of minutes

k = constant of proportionality

After 5 minutes, a bacteria colony has 1.3 million organisms. Using the formula, y = kx

1,300,000 = 5k

k = 1,300,000 / 5

k = 260,000

After 12 minutes, the same colony has 41.5 million organisms. Using y= kx

41,500,000 = 12x

x = 41500000 / 12

x = 3458333.8

After 15 minutes, the colony has grown to 101.3 million organisms.

y = kx

101,300,000 = 15k

k = 101,300,000 / 15

k = 6753333.8

It is a non-proportional relationship as the constant of proportionality is different for each.

Answer:

The shortest combined distance along the path from the flagpole to Clue 1 to Clue 2 and to Clue 3 is approximately 1,031.025 feet

Step-by-step explanation:

The given coordinates of the clues for the treasure hunt are

The location of the first clue = 5 units north of the flag pole

The coordinates is (0, 5)

The location of the second clue = 6 units east of the flag pole

The coordinates is (6, 0)

The location of the final clue = 5 units south of the flag pole

The coordinates is (0, -5)

The flagpole is at the origin

The coordinates of the flagpole is (0, 0)

Each unit on the graph = 50 feet

From the drawing of the treasure hunt created with Microsoft Excel, the shortest distances between the clues are as follows;

The shortest distance between 2 points is a straight line

Therefore

The shortest length from the flagpole to Clue 1 = 5 - 0 = 5 units

The actual distance from the flagpole to Clue 1 = 5 units × 50 feet/unit = 250 feet

The length from Clue 1 to Clue 2= √(6² + 5²) = √(61) units

The actual distance from Clue 1 to Clue 2 = √(61) units × 50 feet/unit = 50·√61 feet

By similarity, the actual distance from Clue 2 to Clue 3 = 50·√61

The combined shortest distance along the path from the flagpole to Clue 1 to Clue 2 and to Clue 3 = (250 + 50·√61 + 50·√61) feet ≈ 1,031.025 feet

There is insufficient evidence to substantiate the publisher's claim at the 0.05 level of significance.

To determine if there is sufficient evidence to substantiate the publisher's claim, we need to conduct a hypothesis test.

Let's assume the null hypothesis is that the proportion of readers who own a personal computer is equal to 0.32.

The alternative hypothesis is that the proportion is greater than 0.32.

We can use a one-tailed z-test for proportions to test the hypothesis.

At the 0.05 level of significance, the critical z-value for a one-tailed test is 1.645.

If our calculated z-value is greater than 1.645, we reject the null hypothesis and conclude that there is sufficient evidence to support the publisher's claim.

Assuming we take a random sample of readers and find that 350 out of 1000 readers own a personal computer, the calculated z-value can be computed as:

\(z = (p - P) / \sqrt( P(1-P) / n )\)

where

p = sample proportion = 350/1000 = 0.35

P = hypothesized proportion = 0.32

n = sample size = 1000

z = (0.35 - 0.32) / sqrt( 0.32 * 0.68 / 1000 )

z = 1.42

Since the calculated z-value (1.42) is less than the critical z-value (1.645), we fail to reject the null hypothesis.

Therefore, there is insufficient evidence to substantiate the publisher's claim at the 0.05 level of significance.

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Answer:

2.421

Step-by-step explanation:

Ill put the numbers in order from largest to smallest:

3

2.905

2.81

2.713

2.421

it's the smallest because it has 2 ones, 4 tenths, 2 hundredths, and 1 thousandth

Answer:

2.421

Step-by-step explanation:

All work is provided in the screenshot attached! :)

In general, if a paired difference experiment is conducted, it typically involves comparing two sets of measurements or observations that are paired in some way, such as before-and-after measurements on the same individuals or measurements on paired individuals in a study.

I'm sorry, but the given information is incomplete as there are no results shown for the paired difference experiment. Without this information, I cannot provide a specific answer to the question. However, to test the hypothesis of interest, a paired t-test is commonly used, which calculates the mean difference between the paired observations and compares it to a hypothesized value using a t-distribution. The p-value of the test is then calculated based on the observed t-statistic and the degrees of freedom, and it represents the probability of obtaining a test statistic as extreme or more extreme than the observed value if the null hypothesis were true. If the p-value is smaller than the chosen level of significance (typically 0.05), the null hypothesis is rejected, and it is concluded that there is evidence in favor of the alternative hypothesis. Conversely, if the p-value is larger than the significance level, the null hypothesis cannot be rejected, and the conclusion is that there is not enough evidence to support the alternative hypothesis.

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Answer:

$220

Step-by-step explanation:

Because, from 1 to 20 there are 10 odd numbers (1, 3, 5, 7, 9, 11, 13, 15, 17, 19) so it is said that for one odd number you win $22, as for 10 odd numbers, that is $22 x 10 which is $220

Answer:

-15 - 3 = -18

Rob owes his father 18 dollars.

Step-by-step explanation:

If he borrowed 15 dollars from his dad, then 3 more, he borrowed a total of 15 + 3 dollars. That means he borrowed a total of 18 dollars. When you borrow money, you owe people, and after you spend the borrowed money it's like subtracting money from your 0 dollars. 0 - 18 = -18. He needs to earn 18 more dollars to pay back his father and get a balance of 0 dollars again.

Hope this helps.

The lowest point should be used for measurement. To acquire a correct reading, students must read the meniscus at eye level. In order to read the meniscus at eye level, students need first set the graduated cylinder on the table and then stoop.

A measuring cylinder, often referred to as a graded cylinder, a cylinder measuring cylinder, or a mixing cylinder, is a piece of lab apparatus used to gauge the quantity of fluids, chemicals, or solutions used during a typical lab session. Compared to common laboratory flasks and beakers, graduated cylinders offer higher precision and accuracy. The graduated cylinder is a scientific tool that employs the metric system rather than the American standard system, so measurements are made in millilitres rather than ounces. The volume of an object or quantity of liquid is measured using a graduated cylinder, a common piece of laboratory glassware. It is a glass cylinder with side markings resembling those on a measuring cup, as its name suggests.

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A satisfaction survey was administered to employees of an automobile company. Not all employees responded to the survey. Of those individuals who responded, 89% reported that they are "satisfied" with their job. Based on this information 89% is considered a/an Statistic.

In statistics, a statistic is a numerical characteristic or measure that is calculated from a sample of data. In this case, the 89% satisfaction rate is calculated from the subset of employees who responded to the survey. It represents a characteristic of the sample, rather than a characteristic of the entire population of employees in the company.

On the other hand, a parameter refers to a numerical characteristic or measure that describes a population as a whole. Since the satisfaction rate of the entire employee population is not known, we cannot consider 89% as a parameter.

Average (a) and deviation (d) are not appropriate options in this context. The 89% satisfaction rate does not represent an average of values or a measure of deviation.

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Answer:

50

Step-by-step explanation:

To calculate the volume of the solid obtained by revolving the region under the graph of `f(x) = x + 2` about the x-axis over the interval `[0, 10]`, we need to use the formula:`V = π∫_a^b▒(f(x))^2dx`

where `a = 0`,

`b = 10`,

`f(x) = x + 2`, and `V` is the volume of the solid.

Let us begin with evaluating the integral:`π∫_0^10▒(x + 2)^2dx`=`π∫_0^10▒(x^2 + 4x + 4)dx`

=`π [ (x^3)/3 + 2x^2 + 4x ]_0^10`

=`π [ ((10)^3)/3 + 2(10)^2 + 4(10) - ((0)^3)/3 - 2(0)^2 - 4(0) ]`

=`π [ (1000/3) + 200 + 40 - 0 - 0 - 0 ]`

=`(1240/3)π`

Therefore, the volume of the solid obtained by revolving the region under the graph of `f(x) = x + 2` about the x-axis over the interval `[0, 10]` is `(1240/3)π`. We can use the method of cylindrical shells to obtain the same result. In this case, the radius of the cylindrical shell is `x + 2`, the height is `dx`, and the thickness is `2πx`. Therefore, the volume of the cylindrical shell is:`dV = 2πx(x + 2)dx` Integrating this expression over the interval `[0, 10]` gives:

` V = ∫_0^10▒2πx(x + 2)dx`

=`2π∫_0^10▒(x^2 + 2x)dx`

=`2π [ (x^3)/3 + x^2 ]_0^10`

=`2π [ ((10)^3)/3 + (10)^2 - ((0)^3)/3 - (0)^2 ]`

=`(1240/3)π`

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Answer:

6 and 2/5

Step-by-step explanation:

20% of 32 is 6.4

(a) The average velocity of the particle over the time interval 1,4 is (1/3) * integral from 1 to 4 of (6 - 2t) dt.

(b) The total distance travelled by the particle over the time interval [1,4] is 5 meters.

(a) The average velocity of the particle over the time interval 1,4 is given by the definite integral:

average velocity = (1/3) * integral from 1 to 4 of (6 - 2t) dt

(b) To find the total distance travelled by the particle over the time interval [1,4], we need to find the area under the velocity-time graph. The velocity-time graph for the particle is a straight line with slope -2 and y-intercept 6. It intersects the t-axis at t = 3, which means the particle comes to a stop at t = 3 and then starts moving in the opposite direction.

Therefore, the total distance travelled by the particle over the time interval [1,4] is the sum of the distances travelled by the particle in the two intervals [1,3] and [3,4].

The distance travelled by the particle in the interval [1,3] is:

distance = integral from 1 to 3 of |6 - 2t| dt
        = integral from 1 to 3 of (2t - 6) dt  [since 6 - 2t is negative in this interval]
        = [-t^2 + 6t] from 1 to 3
        = 4

The distance travelled by the particle in the interval [3,4] is:

distance = integral from 3 to 4 of |6 - 2t| dt
        = integral from 3 to 4 of (2t - 6) dt  [since 6 - 2t is positive in this interval]
        = [t^2 - 6t] from 3 to 4
        = 1

Therefore, the total distance travelled by the particle over the time interval [1,4] is:

total distance = distance travelled in [1,3] + distance travelled in [3,4]
              = 4 + 1
              = 5 meters

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Answer:

4 Thank you cards

Step-by-step explanation:

lmk if you need the work on how i got it :)

(A) If Two independent events, A and B, are such that P(A) = 0. 2 P(A U B) = 0. 8, then probability P(B) =  5/8.

The possibility of the result of any random event is referred to as probability. This term refers to determining how likely an event is to occur. What are the chances of getting a head when we toss a coin in the air, for instance? The quantity of outcomes depends on the response to this question. Here, the outcome could be either head or tail. Thus, there is a 50% chance that the result will be a head.

The probability serves as a gauge for the likelihood that an event will occur. It gauges how likely an event is to occur. The probability equation is given by;

P(E) = Number of Favourable Outcomes/Number of total outcomes

We know that

P(A∪B) = P(A) + P(B) - P(A∩B)

P(A∪B) = P(A) + P(B) - P(A).P(B)

0.8 = 0.2 + P(B) - 0.2.P(B)

0.5 = P(B)  - 0.2.P(B)

0.5 = 0.8.P(B)

P(B) = 0.5/0.8

P(B) = 5/8

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A matrix structure is an adaptation of the divisional structure whereby various divisions or parts of divisions are grouped together based on some common strategic elements, usually linked to distinct product/market differences.

In a matrix structure, organizations create a dual reporting system where employees report to both functional managers and project or product managers. This structure allows for greater flexibility and collaboration across departments, as individuals from different functional areas come together to work on specific projects or initiatives. The matrix structure is often employed in complex organizations that operate in multiple markets or industries, as it enables efficient resource allocation and coordination. By grouping divisions or parts of divisions based on common strategic elements, organizations can streamline decision-making processes and enhance cross-functional communication and cooperation.

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Answer:

A. x < $20 or x > $150

B. x \(\geq\) $25

C. x \(\leq\) 35mph

D. x \(\leq\) $4

Step-by-step explanation:

Not sure of the format desired for item A but this is what I came up with.

Answer:

converting 7.5miles to km.i have...

1mile = 1.6km

7.5miles=xkm...

cross multiplying I have..

xkm=7.5 × 1.6

xkm=12

Answer:

12km

Step-by-step explanation:

5 miles = 8 km

→ Work out how much kilometres in a mile

1 miles = 1.6km

→ Multiply both sides by 7.5

7.5 miles = 12km

Answer:

5.91× 10^ −7

Step-by-step explanation:

Hope this helps