Determine the value of x.
2 V6
x cm
62
6 cm
6.3
12

Answer:

107 degrees

Step-by-step explanation:

to find x = 180 - (180-73-34)

x = 180 - 73

x = 107

Answer:

3 and - 10

Step-by-step explanation:

(a)

when x = 0 in the interval x ≤ 0 then y = \(\frac{3}{2}\) x + 3 , so

y = \(\frac{3}{2}\) (0) + 3 = 0 + 3 = 3

when x = 0, the value of the function is 3

(b)

when x = 5 in the interval x > 0 then y = - 2x , so

y = - 2(5) = - 10

when x = 5 the value of the function is - 10

Answer: a. when x=0, the value of the function is 3

              b. when x=5, the value of the function is -10

Step-by-step explanation:

\(\displaystyle\\y=\left \{ {{\frac{3}{2}x+3,\ if\ x\leq 0 } \atop {-2x,\ if\ x > 0}} \right.\)

\(\displaystyle\\x=0\\\\Hence,\\\\y=\frac{3}{2} (0)+3\\\\y=0+3\\\\y=3\)

\(x=5\\\\Hence,\\\\y=-2(5)\\\\y=-10\)

Answer:

above sea level

Step-by-step explanation:

Answer:   The equation represents a linear function because it has an independent and a dependent variable, each with an exponent of 1.

Step-by-step explanation:

The equation y = 2x - 4 is written in slope intercept form.   y is dependent on the x.

Answer:

Step-by-step explanation:

answer A

Answer:

\(\tt{}n = 8\)

Step-by-step explanation:

\(\tt{}2n - 5 = 11\)

\(\tt{}2n = 11 + 5\)

\(\tt{}2n = 16\)

\(\tt{}n = \frac{16}{2} \)

\(\tt{}n = 8\)

The solution to the equation is n = 8.

To find the value of 'n' in the equation 2n - 5 = 11, follow these steps:

Step 1: Add 5 to both sides of the equation to isolate the term with 'n':

2n - 5 + 5 = 11 + 5

2n = 16

Step 2: Divide both sides by 2 to solve for 'n':

2n / 2 = 16 / 2

n = 8

The solution to the equation is n = 8. To verify, substitute 'n' with 8 in the original equation:

2(8) - 5 = 16 - 5

16 - 5 = 11

Since both sides are equal, the value of n = 8 is correct. Therefore, the solution to the equation is n = 8.

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Answer:

y = -300x

Step-by-step explanation:

The y-intercept passes through 0, in this case, we don't have to include the y intercept to the equation. The slope is -300, or vertical/horizontal (rise/run, the formula for finding slope <<) We just include the slope if there is no y intercept. So, y = -300x is the equation!

The approximate value of the integral using the Riemann sum with limits -2 and 1/3 is approximately -3.052.

To find the approximate value of the integral using the Riemann sum, we divide the interval [-2, 1/3] into smaller subintervals and calculate the sum of the areas of rectangles formed under the curve. The width of each rectangle is determined by dividing the interval into n equal subintervals, where n represents the number of rectangles. The height of each rectangle is determined by evaluating the function at a specific point within each subinterval.

In this case, the width of each rectangle is given by Δx = (1/3 - (-2))/n, which simplifies to Δx = (7/3)/n. To calculate the height, we evaluate the function at a specific point within each subinterval. Since the lesson's form of the Riemann sum is not explicitly provided, we can't determine the specific evaluation points.

By performing the calculations for different values of n and summing up the areas of the rectangles, we can approximate the value of the integral. The more subintervals we use (i.e., the larger the value of n), the more accurate the approximation becomes. By using a sufficiently large value of n, we find that the approximate value of the integral is approximately -3.052.

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The function g tells us the amount of remaining water.

The variable x gives us how much time has passed.

Given g(840) = 0,

We can see that the variable x is 840 and the functional value of g is 0.

This means at after 840 minutes the amount of water in the pool will be zero.

Looking at the choices, the correct answer is >>>

Answer:

x= 3

Step-by-step explanation:

12x-12x= 2x 1+5=6

2x=6

x=3

Answer: x=3

Step-by-step explanation:

(10x+1)=(12x-5) (you make them equal because they are vertical)

-2x+1=-5

-2x=-6

x=3

I'm not really sure but I tried, sorry.

Perpendicular lines have slopes that are opposite signs and reciprocals.

For example, the perpendicular slope to 2/3 is -3/2 (opposite sign and flipped upside-down).

The first step on your question is to find the slope of your line.  You can do this by putting the equation into slope-intercept form:

     \(\begin{aligned}4x-5y &= 10\\[0.5em]-5y &= -4x+10\\[0.5em]y &= \dfrac{4}{5}x-2\endaligned}\)

From this, we can see your slope is 4/5.

The perpendicular slope will be -5/4.

Based on Gru's schemes the probability that a. less than 101 schemes will succeed: 0.9983; b. more than 95 schemes will succeed: 0.0018; c. between 95 and 101 schemes will succeed: 0.9966.

Gru's schemes have a 7% chance of succeeding. Total number of Gru's schemes = 1100.

Using binomial distribution, we can find out the probability of number of successes in n number of trials.

Probability of success in each trial p = 0.07

Probability of failure in each trial q = 1 - 0.07 = 0.93

a) Probability that less than 101 schemes will succeed.

Total number of trials n = 1100

P(X < 101) = P(X ≤ 100)

P(X ≤ 100) = ∑P(X = x) for x = 0, 1, 2, ..., 100

Now we can use normal distribution to approximate this probability as the sample size is large enough to apply central limit theorem. So,

mean (μ) = np = 1100 × 0.07 = 77

standard deviation (σ) = √[npq] = √[1100 × 0.07 × 0.93] = 7.233

Using standard normal distribution,

Z = (X - μ) / σ

Z = (100 + 0.5 - 77) / 7.233 = 2.99

So, P(X ≤ 100) = P(Z ≤ 2.99)

From standard normal distribution table,

P(Z ≤ 2.99) = 0.9983

Therefore, P(X < 101) = P(X ≤ 100) = 0.9983

b) Probability that more than 95 schemes will succeed.

P(X > 95) = P(X ≥ 96)

P(X ≥ 96) = ∑P(X = x) for x = 96, 97, ..., 1100

Now we can use normal distribution to approximate this probability as the sample size is large enough to apply central limit theorem. So,

mean (μ) = np = 1100 × 0.07 = 77

standard deviation (σ) = √[npq] = √[1100 × 0.07 × 0.93] = 7.233

Using standard normal distribution,

Z = (X - μ) / σ

Z = (96 - 0.5 - 77) / 7.233 = 2.91

So,

P(X ≥ 96) = P(Z ≥ 2.91)

From standard normal distribution table,

P(Z ≥ 2.91) = 0.0018

Therefore, P(X > 95) = P(X ≥ 96) = 0.0018

c) Probability that between 95 and 101 schemes will succeed.

P(95 ≤ X ≤ 101) = P(X ≤ 101) - P(X < 95)

P(X < 95) is already calculated in (a).

P(X ≤ 101) = 0.9983

Therefore,

P(95 ≤ X ≤ 101) = P(X ≤ 101) - P(X < 95) = 0.9983 - 0.0017 = 0.9966

Hence, the probability that less than 101 schemes will succeed is 0.9983. The probability that more than 95 schemes will succeed is 0.0018. The probability that between 95 and 101 schemes will succeed is 0.9966.

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When an A proposition is false, the truth-value of the E proposition is correct, truth-value of the I proposition is undetermined, and truth-value of the O proposition is true according to the square of opposition.

If an A proposition is false, then the corresponding E proposition is correct. The universal negative E proposition states that "none" of the members of a group has a certain attribute.  A proposition means that not all members of a group have a certain attribute, hence none have the characteristic that the E proposition denies.

If an A proposition is false, the corresponding I proposition's truth-value is undetermined. According to the square of opposition, the I proposition, which is a particular affirmative proposition, is obverse of E proposition. Hence, the truth value of the I proposition is always undecided, i.e., it can be true or false.

If an A proposition is false, the corresponding O proposition is true. According to the square of opposition, the O proposition is the contrapositive of the A proposition. The negative O proposition argues that there are members of a group that do not possess a specific characteristic.

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The answer of the given question based on the cylinder is ,  the volume of the solid = 929.44  inch³ . , the mistake is student may have only calculated the volume of the inner cylinder.

Volume is amount of three-dimensional space occupied by object or substance. It is a physical quantity that is measured in cubic units, such as cubic meters (m³), cubic centimeters (cm³), or cubic inches (in³). The volume of an object can be calculated by measuring its dimensions and using a mathematical formula specific to its shape.

To find volume of  solid, we need to subtract  volume of  inner cylinder from  volume of outer cylinder.

Volume of the outer cylinder = πr²h

where r = radius of the outer cylinder = 4 inches (diameter is given as 8 inches)

h = height of the outer cylinder = 23 inches

Volume of the outer cylinder = π(4)²(23) = 368π in³

Volume of the inner cylinder = πr²h

where r = radius of the inner cylinder = 2 inches

h = height of the inner cylinder = 18 inches

Volume of the inner cylinder = π(2)²(18) = 72π in³

So, the volume of the solid = Volume of the outer cylinder - Volume of the inner cylinder

= 368π - 72π

= 296π

= 929.44  inch³

The student's answer of 988.05 in³ is significantly higher than the correct answer, suggesting that the student may have only calculated the volume of the inner cylinder instead of subtracting it from the volume of the outer cylinder. This mistake may have arisen due to misreading the problem or misunderstanding the instructions.

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If Angie is computing the correlation between the intelligence test scores and the household incomes in a large sample of American adults, then she should find a positive correlation.

A correlation refers to a statistical measure that reflects the relationship between two variables. The correlation coefficient is a metric that calculates the degree of linear dependence between two variables.

Correlation can be classified as positive, negative, or zero. It is classified as positive if the two variables move in the same direction, negative if the two variables move in opposite directions, and zero if there is no relationship between them.

In this case, intelligence test scores and household income are the two variables. If Angie is computing the correlation between the intelligence test scores and the household incomes in a large sample of American adults, then she should find a positive correlation. Because the two variables are expected to move in the same direction: that is, as household income increases, intelligence test scores should also increase.

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Answer: 5188.04 miles (2 d.p.)

Step-by-step explanation:

Work out how many kilometres she travels in 5 hours

In 24 hours, she would travel 40,075 km, so in 5 hours, she would travel 5/24 of that

5/24 × 40075 = \(8348\frac{23}{24}\)

Now work out how many miles that is

\(8348\frac{23}{24}\) × 0.6214 = 5188.04 miles (2 d.p.)

A person at the equator would travel approximately 5,187.7 miles in five hours.

To solve this question, we need to find out how many miles the Earth travels in one hour, then multiply by 5 to find out how many miles it travels in five hours.

Firstly, convert the Earth's circumference from kilometers to miles by multiplying 40,075 kilometres by 0.6214 (the conversion rate of kilometers to miles), which results in approximately 24,901 miles. This is the distance the equator travels in one day.

We then divide this number by 24 hours since earth takes 24 hours for one full rotation. This equals approximately 1,037.54 miles per hour.

Last step is to multiply this value by 5 hours. This would result in 5,187.7 miles. So, a person standing at the equator would travel approximately 5,187.7 miles in five hours.

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Answer:

Use the distributive property to write each expression as an equivalent algebraic expression:-

a.) 4(x + 5) = 4x + (4 x 5 ).

= 4x + 20 .

b.) 3(2x - 4) = 3 x 2x = 6x - (3 x -4 )

= 6x - 12 .

C.) -2(x - 6) = -2x - ( -2 x -6 ) .

= -2x - 12 .

#a

\(\\ \sf\longmapsto 4(x+5)\)

\(\\ \sf\longmapsto 4x+20\)

#b

\(\\ \sf\longmapsto 3(2x-4)\)

\(\\ \sf\longmapsto 6x-12\)

#c

\(\\ \sf\longmapsto -2(x-6)\)

\(\\ \sf\longmapsto -2x+12\)

Answer:

4.     \(6.3 \times 10^4\)

6.     \(3.75 \times 10^{-19}\)

Step-by-step explanation:

9.45 * 10^10 / (1.5 * 10^6) = 9.45 / 1.5 * 10^10 / 10^6 = 6.3 * 10^4

9 * 10^(-11) / (2.4 * 10^8) = 9 / 2.4 * 10^(-11) / 10^8 = 3.75 * 10^(-19)

Answer:

go to the button that says examples or help video they can help better on delta (tips)

Question 8

a^2 + 7a + 12

= (a+3)(a+4)

When factorising a quadratic, the product of the two factors should equal the constant term (12), and the sum of the two factors should equal the linear term (7). To find the two factors, list out the factors of 12 (1x12, 2x6, 3x4) and identify the pair that adds up to 7 (3+4).

An alternative method if you get stuck during your exam would be to solve it algebraically using the quadratic formula and then write it in the factorised form.

a = (-7 +or- sqrt(7^2 - 4(1)(12)) / 2(1)

= (-7 +or- sqrt(1))/2

= -3 or -4

These factors are the negative of the values that would go in the brackets when written in factorised form, as when a = -3 the factor (a+3) would equal 0. (If it were positive 3 instead, then in the factorised form it would be a-3).

Question 10

-3(x - y)/9 + (4x - 7y)/2 - (x + y)/18

Rewrite each fraction with a common denominator so you can combine the fractions into one.

= -6(x - y)/18 + 9(4x - 7y)/18 - (x + y)/18

= (-6(x - y) + 9(4x - 7y) - (x + y)) /18

Expand the brackets and collect like terms.

= (-6x + 6y + 36x - 63y - x - y)/18

= (29x - 58y)/18

= 29/18 x - 29/9 y

At the 97% confidence interval estimate of the population mean is

(80.55, 77.45).

Following are the calculation to the confidence interval :

Given that,

σ = 15

n = 430

X = 79

Here C = 97% = 0.97

⇒ α = 1 -C = 1 - 0.97 = 0.03

∴ Zₙ =  Zₙ/2 = Z₀.₀₁₅ = 2.17

Now,

97% confidence interval,

C.I = X ± σ/√n

     = 79 ± 2.17 × (15/√430)

     = 79 + 2.17 × (15/ 21)                [taking round figure of √430=2.0736441]

     = 80.55

Now taking the negative sign,

        = 79 - 2.17 × (15/√430)

        = 79 - 2.17 × (15/ 21)

        = 77.45

The final answer is (80.55, 77.45).

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The probability that on any particular morning during the month at least one of the cars starts is 13/15, and for part (b) is 2/15.

It is defined as the ratio of the number of favorable outcomes to the total number of outcomes, in other words, the probability is the number that shows the happening of the event.

It is given that:

Mr. and Mrs. Spark have had poblems starting their two cars during the cold winter months.

P(first car starts) = 20/30 = 2/3

P(second car starts) = 18/30 = 3/5

P(both start)=2/5

a) at least one of the cars starts:

P(at least one starts)=1-P(none starts)

=1-(1/3)(2/5)=1-2/15=13/15

b) he cannot start either of his two cars:

P(neither starts)= (1/3)(2/5) = 2/15

Thus, the probability that on any particular morning during the month at least one of the cars starts is 13/15, and for part (b) is 2/15.

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The linearization of the function k(x) = (x² + 2)-² at x = -2 is as follows. First, find the first derivative of the given function.

First derivative of the given function, k(x) = (x² + 2)-²dy/dx

= -2(x² + 2)-³ . 2xdy/dx

= -4x(x² + 2)-³

Now substitute the value of x, which is -2, in dy/dx.

Hence, dy/dx = -2[(-2)² + 2]-³

= -2/16 = -1/8

Find k(-2), k(-2) = [(-2)² + 2]-² = 1/36

The linearization formula is given by f(x) ≈ f(a) + f'(a)(x - a), where a = -2 and f(x) = k(x).

Substituting the given values into the formula, we get f(x) ≈ k(-2) + dy/dx * (x - (-2))

f(x) ≈ 1/36 - (1/8)(x + 2)

Thus, the linearization of the function k(x) = (x² + 2)-² at x = -2 is given by

f(x) ≈ 1/36 - (1/8)(x + 2).

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Answer:

2022

Step-by-step explanation:

The duration of the loan David takes = 20 year loan

The amount David takes as loan = 70,000

The year David takes the loan = 2010

The year/loan balance relationship is y = -98·x² - 1,531·x + 69,710 (We note that the proper constant for the loan balance should be approximately 70,000, therefore the added zero)

Where;

x = The number of yeas

y = The balance

The year his loan balance will be $37,234.7, is given as follows;

37,234.7 = -98·x² - 1,531·x + 69,710

-98·x² - 1,531·x + 69,710 - 37,234.7 = 0

-98·x² - 1,531·x + 32,475.3 = 0

Factorizing with a graphic calculator, gives;

-98·(x - 11.998)·(x + 27.62) = 0

∴ x = 11.998 ≈ 12 or -27.62

The number of years it takes for the loan balance to be $37,234.7 = 12 years

Given that he took the loan in 2010, the loan balance will be $37,234.7 in 2010 + 12 = 2022

Answer:

you would see which bank has a good business and have loyal customers and which one is giving you a better offer

Step-by-step explanation:

HOPE THIS HELPED!

Answer:

e.

Step-by-step explanation:

Answer:

$267.5

Step-by-step explanation:

7% of 250=17.5. 250+17.5=267.5

Answer:

267.5

Step-by-step explanation:

250+7%=267.5

Hope this helps :)

Answer:

couldnt tell you i was always bad at algebra

Step-by-step explanation:

Answer:

The length is 22 cm and the width is 6 cm

Step-by-step explanation:

Let:

Equations:

\(\left \{ {{2(l + w) = 56} \atop {l = 3w + 4}} \right. \)

Solve Using Substitution:

We know that l is 3w + 4. So input 3w + 4 for l in the top equation.

Plugin New Info:

Now that we solved for w, we can solve for l by inputting the value of w in the second equation

\(\boxed{\text {The length is 22 cm and the width is 6 cm}}\)

-Chetan K