John had to pay a combined electric and gas bill $150. The electric portion of the bill was $90. What is the ratio of money spent on electric to that on gas?

Carolyn made an error in her work because she did not correctly distribute the negative in Step 3.

A system of equations is the given term math for two or more equations with the same variables. The solution of these equations represents the point of the intersection.

You can solve a system of equations by the adding or substitution methods. In the addition method, you eliminate a variable, on the other hand, in the substitution method you replace a variable for the other.

The question gives:3x-2y=7 (1)y=x+2The question shows that Carolyn applies the substitution method because she replaces the variable y (equation 2) in equation 1. See the given step 2.

3x – 2y = 7

3x – 2(x + 2) = 7

3x – 2x - 4 = 7 - here it is the mistake. (Carolyn did not correctly distribute the negative).

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The speed s of Ed's drive to work is 24 mph.

Let d be the distance between Ed's home and work, and let t be the time it takes him to drive to work at speed s. Then, we know that Ed drove half the distance to work before turning around, so he drove d/2 miles.

When he turns around, he increases his speed by 8 mph, so his new speed is s+8 mph. He then drives back to his home, covering the same distance of d/2 miles at an increased speed.

The time it takes him to drive home is therefore (d/2)/(s+8) hours. When he arrives home, he turns around and drives to work at a speed of (s+6) mph. The time it takes him to drive to work is then d/(s+6) hours.

Since Ed's total driving time is 67% greater than usual, we know that his new driving time is 1.67t. Setting up an equation using these values, we get:

d/(s+6) + d/2/(s+8) + d/(s) = 1.67t

Simplifying this equation yields:

d = 6t(s+6)/(7s+24)

We also know that Ed drove half the distance to before turning around, so:

d/2 = st/2

Substituting for d and solving for s yields:

s = 24 mph

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Answer:

the 3rd choice,   10x + 5, looks good

Step-by-step explanation:

a coefficient is the number in front of a variable , so that's 10

a constant is a number w/o a variable ...  so that's 5

I believe that the answer is 10x + 5.

Coefficents are also know as "multipliers". They pair with variables (in this case, that is x). Constants are simply numbers on their own.

Hope that makes sense.

Answer:

1.5 pound ever dollar

Step-by-step explanation:

just calculate

Answer:

2.25 answer

Step-by-step explanation:

9÷4=2.25answer thanks

Answer:

120-90

=30

the change in stock price is $30 per share

You typically split up the middle term if your a-value (the coefficient on x^2) is not 1.

For example, I'd split up the middle term on 3x^2 + 4x – 4,

but not on x^2 + 4x - 12.  

Technically you could on that second one, but you're making a lot of extra and unecessary work for yourself.

Does that make sense?

Answer:

19/9

Step-by-step explanation:

Important concepts and formulas used to solve the following question:

Answering the question

We want to evaluate the following expression given that h = 2/3

3 - h ÷ 3/4

==> plug in h = 2/3

3 - 2/3 ÷ 3/4

==> First we do the division before the subtraction according to PEMDAS. Rather than trying to divide a fraction by another fraction we can use "keep change flip" (dividing a number by a fraction is the same as multiplying the number by the fractions reciprocal)

3 - 2/3 × 4/3

==> multiply 2/3 and 4/3

3 - 8/9

==> simplify

19/9

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\(\huge\text{Hey there!}\)

\(\mathsf{3 - h \div \dfrac{3}{4}}\)

\(\mathsf{= \dfrac{3}{1}- \dfrac{2}{3} \div \dfrac{3}{4}}\)

\(\mathsf{= \dfrac{3}{1}- \dfrac{2}{3}\times\dfrac{4}{3}}\)

\(\mathsf{= \dfrac{3}{1} - \dfrac{2\times4}{3\times3}}\)

\(\mathsf{= \dfrac{3}{1} - \dfrac{8}{9}}\)

\(\mathsf{= \dfrac{3\times 9}{1\times9} - \dfrac{8}{9}}\)

\(\mathsf{= \dfrac{27}{9} - \dfrac{8}{9}}\)

\(\mathsf{= \dfrac{27 - 8}{9 - 0}}\)

\(\mathsf{= \dfrac{19}{9}\rightarrow 2 \dfrac{1}{9}}\)

\(\huge\text{Therefore your answer should be:}\)

\(\huge\boxed{\mathsf{\dfrac{19}{9}\ or \ 2\dfrac{1}{9}}}\huge\checkmark\)

\(\uparrow\large\text{Either of those should work because they are practically the same}\\\large\text{thing}\)

\(\huge\text{Good luck on your assignment \& enjoy your day!}\)

The population size of mountain bighorn sheep after four years will be approximately 374 individuals.

The intrinsic growth rate of a population is the highest possible growth rate without any environmental or other constraints. Exponential growth is a growth pattern that arises when a population increases in size by a set percentage each year. Exponential growth is one method of modeling population growth and is defined by an accelerating growth rate over time.

The mountain bighorn sheep has an intrinsic growth rate of 0.2 per year, and the formula used to estimate the population size after a given number of years is P = P0ert. In this equation, P0 is the initial population size, P is the final population size, e is Euler's number, r is the intrinsic growth rate, and t is the time in years.

Therefore, to calculate the population size of mountain bighorn sheep after four years, we can use the equation as follows: P = P0ert. By substituting the values given in the problem into the equation, we obtain P = 170 x e^(0.2 x 4). Simplifying the equation yields P = 170 x e^0.8, and rounding this number yields P ≈ 373.96.

Hence, the population size of mountain bighorn sheep after four years will be approximately 374 individuals.

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The probability that the sample proportion will be at least 0.375 = 0.8461

Here, te market research firm conducts telephone surveys with a 40% historical response rate.

so, p = 0.4

here, the sample of 400 telephone numbers is n = 400

and \(\hat{p}=0.375\)

The standard deviation would be,

\(\sigma=\sqrt{\frac{p(1-p)}{n} } \\\\\sigma=\sqrt{\frac{0.4(1-0.4)}{400} } \\\\\sigma=0.0245\)

Now we calculate z score :

\(z=\frac{0.375-0.4}{0.0245} \\\\z=-1.0204\)

The probability that the sample proportion will be at least 0.375:

P(\(\hat{p}\) ≥ 0.375)

= P(z > -1.0204)

= 0.8461

Therefore, the required probability is: 0.8461

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The complete question is;

A market research firm conducts telephone surveys with a 40% historical response rate. What is the probability that in a new sample of 400 telephone numbers, at least 150 individuals will cooperate and respond to the questions? In other words, what is the probability that the sample proportion will be at least 150/400 = .375?

Calculate the probability to 4 decimals.

To find f(2) using synthetic division, we set up the synthetic division table with the coefficients of the polynomial:

2 │ 5  -13  4  -2

 │    10 -6 -2

 └───────────

   5  -3 -2  0

The last entry in the bottom row of the table gives the remainder of the division, which is f(2). Therefore, we have:

f(2) = 5(2)³ - 13(2)² + 4(2) - 2 = 40 - 52 + 8 - 2 = -6

So, the value of the function f(x) = 5x³-13x² + 4x-2 at x = 2 is f(2) = -6.

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Using Central Limit Theorem,

the smallest possible value of sample size , n is 452...

let Xi = 1 if item is defective or

Xi = 0 if item is not defective

Now, Xn- hat = 1/n ∑Xᵢ= sample proportion for defective items

we have to calculate smallest value of n we require P( Xn- hat <0.13 ) > 0.99

we have,. E(Xᵢ) = μ = 0.1 and variance (Xᵢ)

= (.1 ) (1 - 0.1) =( 0.1) (0.9) = σ²

Since, Xi are Bernoulli random variables

According to limit theorem ,

Z = (Xₙ- hat - u) √n/ sd ~ N(1;0) approximately when n is large

Therefore,

P ( Xₙ -hat < 0.13)

=> P (( Xₙ-hat - u)√n / sd < (0.13 - 0.1 )√n/ √0.09 )

=> P( Z < 0.03 √n/0.03 ) where Z~N(1;0)

=> P( Z< √n/10)

i.e f( √n/10 > f(2.32 ) = 0.99

=> n/ 100 > (2.32)²

=> n = (2.32)²× 100

=> n > 541.02 ~ 542

Thus, smallest possible value is 542..

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The net annual percentage growth rate of the city population is 0.4%

To calculate the net annual percentage growth rate of a population, we can use the following formula:

Net Annual Percentage Growth Rate = ((Births + Immigrants) - (Deaths + Emigrants)) / Initial Population x 100%

Plugging in the given values, we get:

Net Annual Percentage Growth Rate =\(((100 + 10) - (40 + 30)) / 10,000 x 100%\)

Net Annual Percentage Growth Rate = \((40 / 10,000) x 100%\)

Net Annual Percentage Growth Rate =\(0.4%\)

The net annual percentage growth rate of the city population is 0.4%

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Answer:

The length of the diagonal from P to Q is

\( \sqrt{ {9}^{2} + {12}^{2} + {8}^{2} } = \sqrt{289} = 17\)

Answer:

7

Step-by-step explanation:

Answer:

no answer

Step-by-step explanation:

2(-2)+3=-2

simplify

-4+3=-2

simplify

-1=-2

No answer

If there's something along the lines of no answer and it's multiple choice click that.

Answer:

30

Step-by-step explanation:

if he can make 42 cakes = 7days

therefore x cakes. =5days

you do cross multiplication

i.e. 42x5/7 =30 days

Answer:

I belive that the solution is 2 gallons and 4 cups

Answer:

1c = 0.0625

36x0.0625=2.25 galon = 2 gal 4 cups

Step-by-step explanation:

The infinite series ax/a+x can be written in the form of a summation notation as \(Σ ( (−1)^n * (x^(n+1))/(a^(n+1)))\), which can be used to calculate the sum of the series for any value of x and a.

The infinite series representing ax/a+x can be written as:

\(∑n=0∞(−1)nx^n+1a^n+1\)

The first 5 terms of this series can be calculated as follows:

\(Term 1 = (x/(a+x))Term 2 = -(x^2/a^2+2ax+x^2) 4Term 3 = (x^3/a^3+3a^2x+3ax^2+x^3) Term 4 = -(x^4/a^4+4a^3x+6a^2x^2+4ax^3+x^4)Term 5 = (x^5/a^5+5a^4x+10a^3x^2+10a^2x^3+5ax^4+x^5)\)

The general formula for the infinite series can be written as:

\(∑n=0∞(−1)nx^n+1a^n+1 = (x/(a+x)) - (x^2/a^2+2ax+x^2) + (x^3/a^3+3a^2x+3ax^2+x^3) - (x^4/a^4+4a^3x+6a^2x^2+4ax^3+x^4) + (x^5/a^5+5a^4x+10a^3x^2+10a^2x^3+5ax^4+x^5) + ...\)

The summation notation for this series can be written as:

\(∑n=0∞(−1)nx^n+1a^n+1 = Σ ( (−1)^n * (x^(n+1))/(a^(n+1)))\)

This formula can be used to calculate the sum of the infinite series for any value of x and a.

The infinite series ax/a+x can be written in the form of a summation notation as \(Σ ( (−1)^n * (x^(n+1))/(a^(n+1)))\), which can be used to calculate the sum of the series for any value of x and a.

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The equation of a line in Standard form is:

Where "A", "B" and "C" are Integers ("A" is positive).

The Slope-Intercept form of the equation of a line is:

Where "m" is the slope and "b" is the y-intercept.

In this case you know that:

And knowing that the line passes through the point

You can substitute values and solve for "b":

Then, the equation of this line in Slope-Intercept form is:

Now that you have this equation, you can write it in Standard form as following:

The answer is:

The statement "Because in a randomized controlled trial (RCT), the assignment is random, therefore there is no coverage bias---by definition" g is false because, it is important to consider both randomization and other factors when assessing the potential for bias in an RCT.

Random assignment in an RCT can help to reduce selection bias, but it does not guarantee the absence of coverage bias.

Coverage bias can occur if the participants who are enrolled in the trial do not represent the population to which the results will be generalized.

For example, if the trial only includes participants who are healthier or more compliant than the typical patient, the results may not be applicable to the broader population.

Therefore, it is important to consider both randomization and other factors when assessing the potential for bias in an RCT.

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\(x^3-2x^2-5x +6\\\\=x^3-x^2-x^2+x-6x+6\\\\=x^2(x-1)-x(x-1)-6(x-1)\\\\=(x-1)(x^2 -x -6)\\\\=(x-1)(x^2 -3x +2x -6)\\\\=(x-1)\textbf{[} x(x-3) +2(x-3)\textbf{]}\\\\=(x-1)(x-3)(x+2)\)

The requried, factored form of the given expression is (x - 1)(x - 3)(x + 2).

A number or algebraic expression that evenly divides another number or expression—i.e., leaves no remainder—is referred to as a factor.

To factor the polynomial f(x) = x³ – 2x² – 5x + 6 completely, we can use a combination of the rational root theorem and synthetic division.

We can use synthetic division to test each possible root and see if it is a factor of the polynomial. Starting with x = 2, we have:

2 | 1 -2 -5 6

  | 2 0 -10

  |_____________

1 0 -5 -4

Since the remainder is not zero, x = 2 is not a factor of the polynomial. Continuing with the other possible roots, we find that x = 1 and x = 3 are roots, but x = -1, x = -2, x = -3, and x = -6 are not roots.

Therefore, we can factor the polynomial as follows:

f(x) = x² – 2x² – 5x + 6

= (x - 1)(x - 3)(x + 2)

So the completely factored form of f(x) is f(x) = (x - 1)(x - 3)(x + 2).

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0.60792 liters x 1000 = 607.92 mL

Multiplying the volume in liters by 1000 converts it to milliliters.

Answer:

A. Undefined

Step-by-step explanation:

Any vertical lines' slope is undefined.

Answer:

A. Undefined

Step-by-step explanation:

Because the line is vertical.

ANSWER :

The height of the prism is h = 7 ft

The are of the base is B = 12 ft^2

The perimeter of the base is P = 18 ft

Fill in the formula. S = 2x12 + 18x7

The surface area of the triangular prism is 150 ft^2

EXPLANATION :

The given formula for the surface area is :

where B = Base area

P = perimeter of the bases

h = height of the prism

The height of the prism is h = 7 ft

The base is a triangle with dimensions of b = 8 ft and a height h = 3 ft

The area of a triangle is :

The are of the base is B = 12 ft^2

The perimeter of the base is 5 + 5 + 8 = 18 ft, so P = 18 ft

Substitute the results in the formula :

The correct interpretation of the given confidence interval is: “We are 95% confident that the population mean number of hours adults spend on formal exercise each week lies between 0.45 and 7.94.”


Option (a) is the correct interpretation because a confidence interval provides an estimate of the range within which the true population parameter (in this case, the mean number of hours spent on formal exercise) is likely to fall. The confidence level of 95% indicates that if we were to repeat the sampling process and construct confidence intervals, 95% of those intervals would contain the true population mean.

Therefore, we can say with 95% confidence that the population mean lies within the interval (0.45 hours, 7.94 hours). Option (b) is incorrect because probabilities are not associated with confidence intervals. Options (c) and € refer to the sample mean, not the population mean. Option (d) incorrectly suggests that we know the true population mean is within the interval, whereas the confidence interval provides an estimate of the likely range.

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The rate of each car is 55 miles per hour.

In order to find the rate of each car, we need to follow the given steps :
1. Let's denote the rate of each car as R (in miles per hour).

2. The first car traveled north from 10 a.m. to 4 p.m., which is 6 hours. So, the distance covered by the first car can be represented as 6R.

3. T he second car traveled south from 12 p.m. to 4 p.m., which is 4 hours. So, the distance covered by the second car can be represented as 4R.

4. According to the problem, the total distance between the two cars at 4 p.m. is 550 miles. Therefore, the sum of the distances covered by both cars should equal 550 miles.

5. Now, we can set up an equation: 6R + 4R = 550

6. Combine the terms: 10R = 550

7. Solve for R: R = 550 / 10 = 55

So, the rate of each car was 55 miles per hour.

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Answer:

x= 2\(\sqrt{6}\)

Step-by-step explanation:

To solve this problem we first observe the Pythagoras equation. If a=x and b = 7 are the lengths of the legs of a right triangle and c= \(\sqrt{73}\) is the length of the hypotenuse, then the sum of the squares of the lengths of the legs is equal to the square of the length of the hypotenuse.

This relationship is represented by the formula:

a*a + b*b = c*c

\(x^{2}\) + \(7^{2}\) = \((\sqrt{73} )^2\)

=> x= \(2\sqrt{6}\)

Answer:

-900

Step-by-step explanation:

Given the expressions

The expresion was rewritten using the Distributive property