The length of a rectangular window is 4 more feet than its width w. The perimeter of the window is 64 feet. Write an equation that could be used to find the demensions of the window and determine the length and width of the window.

Answer:

Chart:

x           y

-6         11

3           5

15         -3

-12        15

Step-by-step explanation:

The only things you can plug in are the domain {-12, -6, 3, 15}

Plug in the domain into equation to find y.

-6 :

y = -2/3 (-6) +7

y = +47

y=11

(-6,11)

3:

y = -2/3 (3) +7

y = -2 +7

y = 5

(3, 5)

15:

y = -2/3 (15) +7

y =  -10 +7

y = -3

(15 , -3)

-12:

y = -2/3 (-12) +7

y = 8 + 7

y= 15

(-12,15)

Answer:

1) 11

2) 3

3) -3

4) -12

Step-by-step explanation:

eq(1):

\(y = \frac{-2}{3} x + 7\\\\y - 7 = \frac{-2}{3} x\\\\x = (y - 7)\frac{-3}{2} \\\\x = (7-y)\frac{3}{2} ---eq(2)\)

1) x = -6

sub in eq(1)

\(y = \frac{-2}{3} (-6) + 7\\\\y = \frac{12}{3} + 7\\\\y = 4+7\\\\y = 11\)

2) y = 5

sub in eq(2)

\(x = (7-5)\frac{3}{2} \\\\x = 3\)

3) x = 15

sub in eq(1)

\(y = \frac{-2}{3} 15 + 7\\\\y = \frac{-30}{3} +7\\\\y = -10 + 7\\\\y = -3\)

4)

sub in eq(2)

\(x = (7-15)\frac{3}{2} \\\\x = -8\frac{3}{2}\\ \\x = -12\)

The explicit formula for f^-1 is (x-3)^(1/4) and this is obtained by switching the roles of x and y and solving for y in terms of x.

To find the inverse function of f(x)=x^4+3, we need to switch the roles of x and y, and solve for y.
Let y = x^4+3
Subtract 3 from both sides to get:
y - 3 = x^4
Take the fourth root of both sides to isolate x:
(x^4)^(1/4) = (y-3)^(1/4)
Simplify:
x = (y-3)^(1/4)
So the inverse function of f(x) is:
f^-1 (x) = (x-3)^(1/4)
This is the explicit formula for the inverse function of f(x).
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Answer:

use the formula: mEq = (mg x valence) / atomic or molecular weight

Step-by-step explanation:

In angle A we have supplementary angles, that is

130 + X = 180

X = 180 - 130

X = 50

From the properties of the angles of a triangle - refer to attached,

W = X + 105

as X = 50 - already calculated above, then

W = 50 + 105

The perimeter of the polygon is 20.23 units

The perimeter of a polygon is the sum of the length of its sides.

Given A(0,−2),B(−5,3),C(3,−3) to find the perimeter of the polygon, we proceed as follows.

To find the length of each side of the polygon, we use the distance formula.

So, d = √[(x - x')² + (y - y')²] where

Using the points A(0,−2), B(−5,3), we have that

d₁ = √[(x - x')² + (y - y')²]

d₁ = √[(0 - (-5))² + (-2 - 3)²]

d₁ = √[5² + (-5)²]

d₁ = √[5² + 5²]

d₁ = √[2(5²)

d₁ = 5√2

Using the points A(0,−2), C(3,-3), we have that

d₂ = √[(x - x')² + (y - y')²]

d₂ = √[(0 - (-3))² + (-2 - (-3))²]

d₂ = √[(0 + 3)² + (-2 + 3)²]

d₂ = √[3² + 1²]

d₂ = √[9 + 1]

d₂ = √10

Using the points B(-5,3), C(3,-3), we have that

d₃ = √[(x - x')² + (y - y')²]

d₃ = √[(-5 - 3)² + (3 - (-3))²]

d₃ = √[(-5 - 3)² + (3 + 3))²]

d₃ = √[(-8)² + (6)²]

d₃ = √[64 + 36]

d₃ = √[100]

d₃ = 10

So, the perimeter of the polygon is D = d₁ + d₂ + d₃

= 5√2 + √10 + 10

= 7.071 + 3.162 + 10

= 20.23 units

So, the perimeter is 20.23 units

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Answer:

r=0

Step-by-step explanation:

28=4r+28

Subtract 28 from both sides, you get

4r=0

so, 0/4 is 0, and r=0

Answer:

r is 7

Step-by-step explanation:

because if you do the math you will see r is 7

The polynomial function f(x)=5 (2x+3)(x+4) (x − 2) has exactly 3 zeros. So statement A is correct.

Polynomial is an expression consisting of indeterminates and coefficients, that involves only the operations of addition, subtraction, multiplication, and positive-integer powers of variables

The given polynomial is f(x)=5(2x+3)(x+4) (x − 2)

The roots we can find by using 2x+3=0, x+4=0 and x-2=0

x=-3/2

x+4=0

x=-4

and x=2 are the roots of function.

Roots are nothing but zeros of the polynomial.

The function has exactly 3 zeros.

Hence, the polynomial function f(x)=5 (2x+3)(x+4) (x − 2) has exactly 3 zeros. So statement A is correct.

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Answer:

Option (3)

Step-by-step explanation:

From the graph attached,

For a point (x, y),

x-coordinate shows the planters and y-coordinate show the number of green pepper plants in the planters.

If input value (x-value) for the line is 3,

Output value (y-value) from the graph will be, y = 9.

Therefore, there are 9 green pepper plants in 3 planters.

Therefore, Option (3) is the correct option.

(a) The slope is 6.

(b)the rate of change is 6 hundred pounds per inch of rain.

(c)When 0 inches of rain fall, 4 hundred pounds of tomatoes are harvested.

(a) The slope of the line defined by the equation is the coefficient of x, which is 6.

(b) The rate of change of the function represents how the quantity of tomatoes harvested changes with respect to the amount of rain. In this case, the rate of change is 6 hundred pounds per inch of rain.

(c) Evaluating f(0) means substituting x = 0 into the function. Therefore, we have:

f(0) = 6(0) + 4 = 0 + 4 = 4

The interpretation for f(0) is: When 0 inches of rain fall, 4 hundred pounds of tomatoes are harvested.

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54 cents cost for 9 inches of wire.

Cost rate is the amount that a worker costs the business. For instance, Zack bills $100 per hour and makes $25 per hour in costs. In other words, the corporation pays him $25 for every hour he bills. The profitability of your workers, projects, and employment is determined by cost rates.

The smallest unit of length is the inch (plural: inches). One foot is made up of 12 inches. An inch is equivalent to 2.54 cm in the metric system. For shorter measurements like measuring a pencil's length or an eraser's breadth, inches are utilized.

Wire measuring 16 inches costs 96 cents,

thus the price is 96/16 = 6 cents.

6cents is the cost per inch of wire

so for 9inch the cost will be

9*6 = 54cents will be the cost of 9inch of wire

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The temperature in this city changed by 7.5 degrees Celcius

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

Rate of change = 0.5 degree Celcius daily

Number of days = 15

Using the above as a guide, we have the following:

Total change = Rate of change * Number of days

Substitute the known values in the above equation, so, we have the following representation

Total change = 0.5 * 15

Total change = 7.5

Hence, the total change is 7.5 degrees

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Complete question

The temperature of a City changes by 0.5 degree Celcius daily in the month of February. Summarize how the high temperature in this city changed over the 15 days

Answer:

x: -3, -2, -1, 0, 1

y: 3, 2, 1, 0, -1

Step-by-step explanation:

To find the answers, simply substitute each values of t into the equation given for each x and y.

Answer:

= 30% decrease

Answer:

15

Step-by-step explanation:

a = 3d

Let d=5

a = 3*5

a = 15

Answer:

f'(x) = 15(5x + 3)²

Step-by-step explanation:

using the chain rule to differentiate

f(x) = g(h(x) , then

f'(x) = g'(x) × h'(x)

f(x) = (5x + 3)³

f'(x) = 3(5x + 3)² × \(\frac{d}{dx}\) (5x + 3)

      = 3(5x + 3)² × 5

      = 15(5x + 3)²

Answer:

b

Step-by-step explanation:

bbbb

The bounds for a 95% confidence interval could be option (B) 72 and 79

We know that the 98% confidence interval has bounds of 73 and 80. This means that if we were to repeat the same experiment many times, we would expect that 98% of the time, the true population mean would fall within this range.

To find the bounds for a 95% confidence interval, we can use the fact that a higher confidence level corresponds to a wider interval, and a lower confidence level corresponds to a narrower interval.

Since we want a narrower interval for a 95% confidence level, we can expect the bounds to be closer to the sample mean. We can calculate the sample mean as the midpoint of the 98% confidence interval

(sample mean) = (lower bound + upper bound) / 2 = (73 + 80) / 2 = 76.5

Next, we can use the formula for a confidence interval:

(sample mean) ± (z-score) × (standard error)

where the z-score depends on the desired confidence level, and the standard error depends on the sample size and sample standard deviation. Since we don't have this information, we can assume that the sample size is large enough (i.e., greater than 30) for the central limit theorem to apply, and we can use the formula

standard error = (width of 98% CI) / (2 × z-score)

For a 98% confidence interval, the z-score is 2.33 (found using a standard normal distribution table or calculator). Plugging in the values, we get

standard error = (80 - 73) / (2 × 2.33) = 1.70

Now, we can use this standard error to calculate the bounds for a 95% confidence interval

(sample mean) ± (z-score) × (standard error) = 76.5 ± 1.96 × 1.70

Simplifying, we get

(lower bound) = 76.5 - 3.33 = 73.17

(upper bound) = 76.5 + 3.33 = 79.83

Therefore, the correct option is (B) 72 and 79

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From the given graph, the numeric values of the expressions are given as follows:

To find the numeric value of a function, we replace each instance of the variable in the function by the desired value.

On the graph of the function, the equivalent to this is that we have to find where the x-axis has the value, and find the value of y for which the function passes through the y-axis.

From the graph, when x = -1, f(x) passes the point at y = 12, hence f(-1) = 12.

For the second item, applying the same logic, we have that:

Hence:

f(1) - g(1) = 10 - 2 = 8.

For the third item, we have to look at the graph of g(x), and find the value of x when y = 4, hence g(x) = 4 when x = 2.

For the fourth item, the functions intersect at point (3,8), hence f(x) = g(x) when x = 3.

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The probabilities of at least 10 are repairable is 1/3. and probabilities of from 3 to 8 are repairable is 1/5*8/15 and probabilities of exactly 5 are repairable is 1/3.

According to the statement

we have given that If 15 actuators have failed and we have to find the probabilities on some conditions.

we know that the formula of probabilities is

probability = possible outcomes / total outcomes

So,

at least 10 are repairable = 1 - 10/15

at least 10 are repairable = (15 - 10)/15

at least 10 are repairable = (5)/15

at least 10 are repairable = 1/3

from 3 to 8 are repairable = 1/5 *8/15

exactly 5 are repairable = 1/3

These are the probabilities of the given conditions.

So, The probabilities of at least 10 are repairable is 1/3. and probabilities of from 3 to 8 are repairable is 1/5*8/15 and probabilities of exactly 5 are repairable is 1/3.

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True. In an inductive argument, the conclusion of the inductive step, p(n+1), is demonstrated by substituting n+1 for n in the statement p(n). Inductive reasoning involves making generalizations based on specific instances or patterns observed. In mathematical induction, we aim to prove a statement is true for all natural numbers or a particular subset of numbers.

The process of mathematical induction consists of two steps: the base case and the inductive step. In the base case, we show that the statement p(1) or p(n0) is true for the lowest value in the considered range, typically n=1 or a specific starting value n0. The inductive step involves assuming the statement p(n) is true for some arbitrary value n=k, and then proving that p(k+1) is also true under this assumption. This is achieved by substituting n+1 for n in the statement p(n).

By confirming both the base case and inductive step, we can conclude that the statement p(n) is true for all natural numbers or the specified subset of numbers. Thus, it is correct to say that the conclusion of the inductive step, p(n+1), is shown by substituting n+1 for n in the statement p(n).

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Answer:

#1

Use Pythagorean:

Apply to given and find c:

#2

#3

We have:

We know that:

Find b:

So

#4

Given

We know that:

Find b:

So

#5

Given

We know:

From the cot we have:

Hypotenuse is:

So,

The total Chi-Square Test Statistic is 6.25.

Chi-square test is a statistical technique that is used to compare the expected and observed values of a categorical data to check for the statistical significance of the difference.

Given that category, obs. freq, expected freq and contribution to Chi Square are provided below:

Category:  

Obs. Freq,   Expected Freq, Contribution to Chi Square.

Refrigerator   70   60   1.6667.

Dish Washer   50   40   2.5.

Range   20   30   3.3333.

Clothes Washer   30   40   2.5.

Clothes Dryer   30   30   0.0.

The formula for calculating the total chi-square test statistic is given by;

X² = ∑ (observed frequency - expected frequency)² / expected frequency

Where;

Σ = Sum of Total frequency = 70+50+20+30+30= 200

Total Expected Frequency = 60+40+30+40+30 = 200

So the total Chi-square Test Statistic is;

\(X²= [(70-60)²/60] + [(50-40)²/40] + [(20-30)²/30] + [(30-40)²/40] + [(30-30)²/30]X² = [100/60] + [25/40] + [100/30] + [25/40] + [0/30]X² = 1.6667 + 0.625 + 3.3333 + 0.625 + 0X² = 6.25\)

Therefore, the total Chi-Square Test Statistic is 6.25.

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(a) The volume of the paint in the can is approximately 0.003086 cubic meters.

(b) The thickness of the layer of wet paint on the wall is approximately 0.06182 meters.

:(a) To convert the volume of the paint from gallons to cubic meters, we need to use the conversion factor 1 U.S. gallon = 0.00378541 cubic meters. Given that the paint can has 0.816 U.S. gallons of paint left, we can calculate the volume in cubic meters by multiplying 0.816 by the conversion factor. The result is approximately 0.003086 cubic meters.

(b) To find the thickness of the layer of wet paint on the wall, we need to divide the volume of the paint (in cubic meters) by the area of the wall (in square meters). The remaining paint can cover an area of 13.2 square meters, so dividing the volume of the paint (0.003086 cubic meters) by the wall area (13.2 square meters) gives us approximately 0.0002333 meters or 0.06182 meters when rounded.

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Answer: $1,146 billion

Step-by-step explanation:

First find the number of years between 2004 and 2017.

= 2017 - 2004

= 13 years

To find out such answers, use the future value formula which shows the value of an amount being increased by a certain percentage over a number of periods.

Future value = Amount * ( 1 + rate) ^ number of periods

= 500 * ( 1 + 5%) ¹⁷

= $1,146 billion

IBM's Cost of Equity based on DGM is 11.46%.

Dividend growth model (DGM) refers to a valuation model used to estimate the price of an investment using predicted dividends and expected growth rates of dividends over a particular period. The equation for DGM is as follows:

P = D1 / (Ke - G)

where:

P = The price of the stock

D1 = The expected dividend to be paid at the end of the year

Ke = The cost of equity

G = The expected dividend growth rate

Therefore, to determine IBM's Cost of Equity based on DGM we can use the given information as follows:

D1 = $4.50

G = 8.00%

Ke = ?

P = $130

Therefore,

Ke = (D1 / P) + G

Ke = ($4.50 / $130) + 0.08

Ke = 0.0346 + 0.08

Ke = 0.1146

Ke = 11.46%

Therefore, IBM's Cost of Equity based on DGM is approximately 11.46%

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Answer:

you find the point where the line intersects

Answer:

yes

Step-by-step explanation:

Answer:  It's an algebraic expression

Step-by-step explanation:  k²- 11 is an algebraic expression.

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