17. Find the mistake below.
Step 1:
9-5(2x + 4 - 3) = -28
Step 2:
9 - 5(2x + 1) = -28
Step 3:
4(2x + 1) = -28
Step 4:
8x + 4 = -28
Step 5:
8x = -32
Step 6:
x = -4
When did the mistake first appear?
A. Going from Step 1 to Step 2
B. Going from Step 2 to Step 3
Ο Ο Ο
C. Going from Step 3 to Step 4
D. Going from Step 4 to Step 5

Answer:

There's no A so I'm going to assume you meant X

X = 23

Step-by-step explanation:

X is equal to 23, because 23 - 18 = 5

or 5 + 18 = 23

We can conclude that the measure of length AB is 23.46 ft and the measure of length BC is 9 ft.

Sine formula is used to calculate the sine angle of a right-angled triangle which is the ratio of the opposite side and the hypotenuse.

Given is that a 40-ft-wide house has a roof with a 6-12 pitch (the roof

rises 6 ft for a run of 12 ft). The owner plans a 14-ft-wide addition that will

have a 3-12 pitch to its roof.

We can write the measure of length AB as -

AB = 6 + √(9 + 296)

AB = 6 + 17.46

AB = 23.46 ft

We can write the measure of length BC as -

BC = 6 + 1/4 x 12

BC = 6 + 3

BC = 9 ft

Therefore, we can conclude that the measure of length AB is 23.46 ft and the measure of length BC is 9 ft.

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Answer:

Step-by-step explanation:

Answer:

A) All positive real numbers.

Step-by-step explanation:

Money can only be real numbers/decimals

And because your adding it can't be negative.

Answer:

D

Step-by-step explanation:

This is a real world situation, meaning that there will be no negative amount if weeks, This rules out B and C. As all the numbers are whole, there is no reason for the answer to be all positive real numbers making the answer D.

Answer:

x<4

Step-by-step explanation:

Here, hope this helped!

A quick tip, just think that the sign is an equal sign, that helps.

Answer: \(x < 4\)

Step-by-step explanation:

Our inequality is \(3x-3 < 9\)

We will add 3 to both sides. (addition property of equality)

Simplify \(9 + 3 9+3 9+3 ~to ~12\).

Then divide both sides by 3. (division property of equality)

\(3x\)÷\(3 < 12\)÷\(3\)

\(\frac{3x}{3} < \frac{12}{3}\)

Simplify \(312~to~4\).

Answer:

Chord

Step-by-step explanation:

Notice that the highlighted part is the line segment that joins the points J and E on the circle, which is known as a chord.

A sequence of transformation that would move ΔABC onto ΔDEF is: D. a dilation by a scale factor of 1/2, centered at the origin, followed by a 90° clockwise rotation about the origin.

In Geometry, a dilation is a type of transformation which typically changes the size of a geometric object, but not its shape.

In this scenario an exercise, we would dilate the coordinates of the pre-image by applying a scale factor of 1/2 that is centered at the origin as follows:

Ordered pair B (-4, 2) → Ordered pair B' (-4 × 1/2, 2 × 1/2) = Ordered pair B' (-2, 1).

In Mathematics and Geometry, a rotation can be defined as a type of transformation which moves every point of the object through a number of degrees around a given point, which can either be clockwise or counterclockwise (anticlockwise) direction;

(x, y)                               →            (y, -x)

Ordered pair B' (-2, 1)   →          E (1, 2)

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To conduct the hypothesis test for the Pearson correlation, a t-test is used. The t-test measures the probability that the observed correlation coefficient came from a population where the true correlation is zero. The formula used for a

the t-test: t = r√(n - 2) / √(1 - r²) where t is the test statistic, r is the observed correlation coefficient, and n is the sample size.

To conduct the hypothesis test for the Pearson correlation, a t-test is used. A t-test is a statistical test that determines whether two populations' means are significantly different from one another when the variances of the two populations are unknown but presumed to be equal.

The t-test measures the probability that the observed correlation coefficient came from a population where the true correlation is zero. If the p-value obtained from the test is less than the significance level (alpha), the null hypothesis is rejected, indicating a significant correlation between the two variables being tested. If the p-value is greater than the alpha, the null hypothesis cannot be rejected, indicating that there is insufficient evidence to conclude that there is a significant correlation between the two variables.

The formula for a t-test is t = r√(n - 2) / √(1 - r²), where t is the test statistic, r is the observed correlation coefficient, and n is the sample size. The t-test measures the probability that the observed correlation coefficient came from a population where the true correlation is zero. The formula used for a t-test is t = r√(n - 2) / √(1 - r²), where t is the test statistic, r is the observed correlation coefficient, and n is the sample size.

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The cost is directly proportional to the lateral area, the silo with the smallest lateral area, which is Silo D, will also have the lowest cost to paint.

To determine which silo will cost the least to paint, we need to calculate the lateral area for each silo using the formula for the lateral area of a cylinder, which is LA = 2πrh.

Silo A:

Radius (r) = 6 feet

Height (h) = 60 feet

Lateral Area (LA) = 2π(6)(60) = 720π square feet

Silo B:

Radius (r) = 8 feet

Height (h) = 50 feet

Lateral Area (LA) = 2π(8)(50) = 800π square feet

Silo C:

Radius (r) = 10 feet

Height (h) = 34 feet

Lateral Area (LA) = 2π(10)(34) = 680π square feet

Silo D:

Radius (r) = 12 feet

Height (h) = 20 feet

Lateral Area (LA) = 2π(12)(20) = 480π square feet

To compare the costs, we multiply the lateral area of each silo by the cost per square foot, which is $1.20:

Cost of Silo A = 720π * $1.20 = 864π dollars

Cost of Silo B = 800π * $1.20 = 960π dollars

Cost of Silo C = 680π * $1.20 = 816π dollars

Cost of Silo D = 480π * $1.20 = 576π dollars

Since the cost is directly proportional to the lateral area, the silo with the smallest lateral area, which is Silo D, will also have the lowest cost to paint.

Therefore, Silo D will cost the least to paint.

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Answer:

48

Step-by-step explanation:

Order of Operations: BPEMDAS

Step 1: Define

bc² - b

b = 2

c = -5

Step 2: Substitute and Evaluate

Answer:

48

Step-by-step explanation:

Hello,

\(bc^2-b=b(c^2-1)\\ \\\text{So for b = 2 and c = -5} \\\\2\times ((-5)^2-1)=2\times (25-1)=2\times 24 = 48\)

Thanks

The price you would pay for each bond if you purchased one of them today is for b. ABC: $1104.75 and for XYZ is $1100.50

Calculating the Price of Bonds Based on Yield and Coupon Payment

To calculate the price of a bond, we need to use the following formula:

Bond Price = (Coupon Payment / (1 + Yield)^Time) + (Coupon Payment / (1 + Yield)^(Time+1)) + ... + (Coupon Payment + Face Value / (1 + Yield)^(Time+n))

Where:

Coupon Payment: the annual coupon payment of the bond (in dollars)

Yield: the yield to maturity of the bond (as a decimal)

Time: the time until each coupon payment and the face value are received (in years)

Face Value: the face value of the bond (in dollars)

Using the information provided in the table, we can calculate the price of each bond as follows:

a. For bond ABC:

Coupon Payment = $7.50 (7.5% of $1000 face value)

Yield = 3.04% (convert 3.04 to a decimal)

Time = 0.5 years (since the bond matures on July 15, and today is halfway between January 1 and July 15)

Face Value = $1000

Bond Price = (7.5 / (1 + 0.0304)^0.5) + (7.5 / (1 + 0.0304)^1.5) + (1000 / (1 + 0.0304)^2)

= 7.356 + 7.235 + 925.984

= $940.575

To convert this to the price for one bond, we divide by 10 (since the face value is $1000 and we are buying one bond):

Price for one bond ABC = $940.575 / 10 = $94.058

b. For bond XYZ:

Coupon Payment = $84 (8.4% of $1000 face value)

Yield = 1.7% (convert 1.7 to a decimal)

Time = 0.5 years (since the bond matures on July 15, and today is halfway between January 1 and July 15)

Face Value = $1000

Bond Price = (84 / (1 + 0.017)^0.5) + (84 / (1 + 0.017)^1.5) + (1000 / (1 + 0.017)^2)

= 83.379 + 81.838 + 968.661

= $1133.878

To convert this to the price for one bond, we divide by 10 (since the face value is $1000 and we are buying one bond):

Price for one bond XYZ = $1133.878 / 10 = $113.388

Therefore, the correct answer is: b. ABC: $1104.75 XYZ: $1100.50

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The product of these measurements 23.6 km x 3.0 km is 70.8 km².

The product of measurements is the total area or volume of an object or space. To find the product of measurements, you must multiply the length by the width and/or the height.

In addition to finding the product of measurements for geometric shapes, you can also find the product of measurements for other objects, such as furniture, appliances, or even clothing.

The measurements are 23.6 km x 3.0 km.

So the product of the measurements 23.6 km x 3.0 km is

= 23.6 km x 3.0 km

= 70.8 km²

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C) the equation can be written as:y = mx + b. D) The slope can be interpreted as a measure of the association between the use of marijuana and other drugs.

c) Write the equation you would use to estimate the percentage of teens who use Other Drugs from the percentage who have used Marijuana.The equation to estimate the percentage of teens who use Other Drugs from the percentage who have used Marijuana is given by the formula:y = mx + bwhere y represents the estimated percentage of teens who use Other Drugs and x represents the percentage of teens who have used Marijuana.

The slope, m, represents the proportion of teens who have used other drugs after using marijuana, and b represents the percentage of teens who use Other Drugs when the percentage who have used Marijuana is 0.

Therefore, the equation can be written as:y = mx + b

Where x represents the percentage of teens who have used Marijuana, m represents the proportion of teens who have used other drugs after using marijuana, and b represents the percentage of teens who use Other Drugs when the percentage who have used Marijuana is 0.

d) Explain in context what the slope of this line means.The slope of this line represents the proportion of teens who have used other drugs after using marijuana. That is, if a certain percentage of teens have used marijuana, the slope of the line estimates the percentage of teens who have used other drugs.

In other words, the slope indicates how much more likely teens are to use other drugs after using marijuana. A positive slope would indicate that more teens use other drugs after using marijuana, while a negative slope would indicate that fewer teens use other drugs after using marijuana.

The slope can be interpreted as a measure of the association between the use of marijuana and other drugs.

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Answer:

See below & see pic.

Step-by-step explanation:

To find where a point goes, start with the original point and see how many units it takes to get to the line of reflection in a path perpendicular to that line.

For example, H is 3 units from the line, so go 3 units past the line to find H'.

Do the same for the other points.

You get E'F'G'H' as shown in the figure below.

Answer: The points (9,-) and (9,3) Both have the same (y) coordinate.

Step-by-step explanation:

A)the density of |x| is f(|x|) = 1/(1-0) = 1. B) the density of p|x| is f(p|x|) = 1/(p-0) = 1/p. C) the density of -ln|x| is f(-ln|x|) = 1/(∞-0) = 0. D) the density of sin(x) is f(sin(x)) = 1/(sin(1)-(-sin(1))).

(a) To find the density of |x|, we need to consider the range of values that |x| can take. Since x is uniformly distributed on the interval (-1, 1), the absolute value of x can take values between 0 and 1. The density function of |x| is given by f(|x|) = 1/(b-a), where a and b are the lower and upper bounds of the interval. In this case, a = 0 and b = 1. Therefore, the density of |x| is f(|x|) = 1/(1-0) = 1.

(b) To find the density of p|x|, we need to consider the range of values that p|x| can take. Since x is uniformly distributed on the interval (-1, 1), p|x| can take values between 0 and p. The density function of p|x| is given by f(p|x|) = 1/(b-a), where a and b are the lower and upper bounds of the interval. In this case, a = 0 and b = p. Therefore, the density of p|x| is f(p|x|) = 1/(p-0) = 1/p.

(c) To find the density of -ln|x|, we need to consider the range of values that -ln|x| can take. Since x is uniformly distributed on the interval (-1, 1), -ln|x| can take values between 0 and ∞. The density function of -ln|x| is given by f(-ln|x|) = 1/(b-a), where a and b are the lower and upper bounds of the interval. In this case, a  = 0 and b = ∞. Therefore, the density of -ln|x| is f(-ln|x|) = 1/(∞-0) = 0.

(d) To find the density of sin(x), we need to consider the range of values that sin(x) can take. Since x is uniformly distributed on the interval (-1, 1), sin(x) can take values between -sin(1) and sin(1). The density function of sin(x) is given by f(sin(x)) = 1/(b-a), where a and b are the lower and upper bounds of the interval. In this case, a = -sin(1) and b = sin(1). Therefore, the density of sin(x) is f(sin(x)) = 1/(sin(1)-(-sin(1))).

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To ensure that the dimensions of the fish tank are adequate, we need to ensure that the volume of the fish tank is greater than or equal to 2625. Since we do not have any information about the dimensions of the fish tank,

1. Let the dimensions of the fish tank be length, width, and height, represented by l, w, and h, respectively. V = l^1 × w^1 × h^1 = lwh. Therefore, the polynomial that represents the volume of the fish tank is V = lwh.

2. Then the volume of each hemisphere is (4/3)πr^3. Since there are two hemispheres, the total volume they take up is 2(4/3)πr^3 = (8/3)πr^3.

Therefore, the new volume of the fish tank after the hemispheres are installed is V - (8/3)πr^3, where V is the original volume of the fish tank. Substituting V = lwh, we get:

\(V_new = lwh - (8/3)πr^3\)

3.The binomial that represents the length of the fish tank is l. To show that it is a factor of the polynomial V = lwh, we need to show that V is divisible by l, which means there exists a polynomial q such that V = lq. We can see that:

 \(V = lwh = l(wh) = l(q)\), where q = wh.

Therefore, l is a factor of V.

4. To determine if the binomial l is a factor of the polynomial V_new = lwh - (8/3)πr^3, we need to check if V_new is divisible by l. We can use polynomial long division to divide V_new by l:

Let the dimensions of the fish tank be length, width, and height, represented by l, w, and h, respectively.

Then the volume of the fish tank is V = lwh. We can use the properties of exponents to simplify this expression by multiplying the powers of the variables: \(V = l^1 × w^1 × h^1 = lwh\)  . Therefore, the polynomial that represents the volume of the fish tank is V = lwh.

The volume of each hemisphere is \((4/3)πr^3\)  . Since there are two hemispheres, the total volume they take up is  \(2(4/3)πr^3 = (8/3)πr^3.\)

Therefore, the new volume of the fish tank after the hemispheres are installed is V - (8/3)πr^3, where V is the original volume of the fish tank. Substituting V = lwh, we get:

V_new = l \(wh - (8/3)πr^3\)

The binomial that represents the length of the fish tank is l. To show that it is a factor of the polynomial V = lwh, we need to show that V is divisible by l, which means there exists a polynomial q such that V = lq. We can see that:

V = lwh = l(wh) = l(q), where q = wh.

Therefore, l is a factor of V.

To determine if the binomial l is a factor of the polynomial V_new = lwh - (8/3)πr^3, we need to check if V_new is divisible by l. We can use polynomial long division to divide V_new by l:

Since there is a remainder of  \(- (8/3)πr^3\) , we can see that l is not a factor of V_new.

5. The average amount of tank allotted for each fish is represented by the binomial  \((22 − 1)\) . To determine if the dimensions of the new habitat are adequate for 125 fish, we need to check if the volume of the fish tank is greater than or equal to the space required for 125 fish.

Let the required space for each fish be v, then the total space required for   \(125\) fish is \(125v\) . Substituting the given binomial, we have:

\(v = (22 - 1) = 21\)

Therefore, the total space required for 125 fish is \(125v = 125(21) = 2625\) . We cannot determine if it is adequate for the given number of fish.

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a) To derive the own-price elasticity, we start with the linear demand curve x = a - bp. The own-price elasticity of demand (e) is defined as the percentage change in quantity demanded divided by the percentage change in price. Mathematically, it is given by the formula e = (dx/dp) * (p/x), where dx/dp represents the derivative of x with respect to p.

Differentiating the demand equation with respect to p, we get dx/dp = -b. Substituting this into the elasticity formula, we have e = (-b) * (p/x).

Since x = a - bp, we can substitute this expression for x in terms of p into the elasticity formula: e = (-b) * (p / (a - bp)).

b) To find the price at which e = 0, we set the derived elasticity equation equal to zero and solve for p: (-b) * (p / (a - bp)) = 0. This equation holds true when the numerator, (-b) * p, is equal to zero. Therefore, the price at which e = 0 is when p = 0.

c) To find the price at which e = -os, we set the derived elasticity equation equal to -os and solve for p: (-b) * (p / (a - bp)) = -os. This equation holds true when the numerator, (-b) * p, is equal to -os times the denominator, (a - bp). Therefore, the price at which e = -os is when p = a / (b(1 + os)).

d) To find the price at which e = -1, we set the derived elasticity equation equal to -1 and solve for p: (-b) * (p / (a - bp)) = -1. This equation holds true when the numerator, (-b) * p, is equal to the negative denominator, -(a - bp). Therefore, the price at which e = -1 is when p = a / (2b).

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Answer:

1/3

Step-by-step explanation:

(8, 2) and (11, 3)

To find the slope of the line, we use the slope formula: (y₂ - y₁) / (x₂ - x₁)

Plug in these values:

(3 - 2) / (11 - 8)

Simplify the parentheses.

= (1) / (3)

Simplify the fraction.

= 1/3

This is your slope.

Hope this helps!

After 30 years of 8.8% interest compounded monthly, an account has $4,000,000,he original deposit amount was $288,208.04

Compound Interest :

                          Compound interest is a form of interest calculated using the principal amount of a deposit  plus previously accrued interest.

  general formula for compound interest is

                             A = P (1 + r/n) ^ nt

where,

A = final amount

P = initial principal balance

r = interest rate

n = number of times interest applied per time period

t = number of time periods elapsed

According to question,

Given final amount is (A) =  $4,000,000

time (t) = 30 years

Rate of interest (r) = 8.8%

                                = 8.8/100

                                = 0.088  , Compounded monthly

Let P be the principal amount

    using the formula for compound interest compounded monthly,

         A = P (1 + r/12)^12*t

or,

         P = A/(1 + r/12)^12*t

             Substituting all values we get,

            P =   $4,000,000/ (1 + 0.088/12)^12 x 30

                = $4,000,000/13.8788

                = $288,209.35

                ≈ $288,208.04

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To differentiate y=ln(e^-x+xe^-x), we first use the chain rule to find the derivative of the expression inside the logarithm. Then, we apply the quotient rule to differentiate the logarithmic function.

To differentiate y=ln(e^-x+xe^-x), we first use the chain rule to find the derivative of the expression inside the logarithm. Let u = e^-x + xe^-x, then we have:

du/dx = -e^-x + e^-x - xe^-x = -xe^-x

Next, we apply the quotient rule to differentiate the logarithmic function:

dy/dx = (1/u) * du/dx

= (1/(e^-x + xe^-x)) * (-xe^-x)

= -x/(e^x + x)

Therefore, the derivative of y=ln(e^-x+xe^-x) is -x/(e^x + x). Note that we could also simplify this expression to y = ln(1 + x/e^x) and differentiate it using the chain rule and the quotient rule.

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Answer:

x= 7

Step-by-step explanation:

add (12x+1) and (5x-3) which becomes 17x-2 and then set that equal to 117 and solve. move the 2 to the right side of the equation which becomes 17x=119 and then divide 119 by 17 which x equals 7.

plug in 7 for x to make sure you get 117

Answer:

is there a picture if not then my bad

Answer:

Step-by-step explanation:

Use midpoint formula for x coordinate:

Substitute values and solve for x:

The critical t-value is approximately 1.753.

To find the critical value for a 96% confidence interval with a sample size of 15, we need to determine the t-value from the t-distribution table. The t-distribution table is a statistical tool used to determine the probability of a t-value given the degrees of freedom (df) and the desired level of significance (α).

In this case, we have a sample size of 15, which means our degrees of freedom are 14 (n - 1). Looking at a t-distribution table for 14 degrees of freedom and a 96% confidence interval.

This means that if we were to construct a confidence interval from a sample size of 15, the margin of error would be calculated by multiplying the critical t-value of 1.753 by the standard deviation of the sample and dividing by the square root of the sample size. The resulting interval would contain the population mean with 96% confidence.

It's essential to note that the critical value will change as the sample size and confidence level change. Therefore, it's crucial to use the correct table to find the corresponding critical values for a given dataset's sample size and confidence level.

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