please help! show all steps ​

Answer:

19 - R = C

7

Step-by-step explanation:

Let R = the number of cars rented

Let C = the number of cars left

19 - R = C

19 - 12 = 7

Answer:

y = .75x + .25

Step-by-step explanation:

I graphed it and expiramrntec with different slopes

Answer:

B. No, Hannah should have used the ratio \( \frac{adjacent}{opposite} \)

Step-by-step explanation:

✍️The formula for calculating cotangent of an angle is given as:

\( cot = \frac{adjacent}{opposite} \).

The ratio, \( \frac{opposite}{adjacent} \), used by Hannah is the formula for calculating tangent of an angle.

Therefore, Hannah did not calculate the cotangent of the angle correctly.

She should have used, the ratio, \( \frac{adjacent}{opposite} \) instead.

Answer:

Step-by-step explanation:

The first part of A is easy. Look at the quadratic function, and the constant, the very last number with no t stuck to it represents the height from which the object in question was originally launched. Our constant is 40, so the height of the roof from which the baseball was thrown is 40 feet. Part 2 of A is not quite as simple because it requires factoring using the quadratic formula.Before we do that, let's make our numbers a bit more manageable, shall we? Let's factor out a -8 to get

\(f(t) = -(t^2-6t-5)\) and a = 1, b = -6, c = -5.

Filling in the quadratic formula now looks like this:

\(t=\frac{6+-\sqrt{6^2-4(1)(-5)} }{2(1)}\) and

\(t=\frac{6+-\sqrt{36+40} }{2}\) and

\(t=\frac{6+-\sqrt{56} }{2}\) so the 2 solutions are

\(t=\frac{6+\sqrt{56} }{2}=6.74sec\) and

\(t=\frac{6-\sqrt{56} }{2}=-.742sec\) and since we know time can NEVER be negative, the time it takes for the baseball to hit the ground from a height of 40 feet is 6.74 seconds. Onto part B.

In order to determine exactly how high the baseball did go, we have to find the vertex of the function. We do this by completing the square and getting the function into vertex, or work, form. Begin by setting the quadratic equal to 0, moving over the constant, and then factoring out the leading coefficient. The rule for completing the square are kinda picky in that you have to have a 1 as the leading coefficient, and righ now ours is a -8. So following the rules I stated above:

\(-8(t^2-6t)=-40\) Next is the take half the linear term, square it, and then add it to both sides. Our linear term is a -6. Half of -6 is -3, and -3 squared is 9, so we add 9 into the parenthesis first:

\(-8(t^2-6t+9)=-40+??\)

Because this is an equation, we can't add 9 to one side without adding the equivalent to the other side. But, we cannot forget about that -8 sitting out front there, refusing to be ignored. We didn't just add in a 9, we actually added in a -8 times 9 which is -72. That's what goes on the right side in place of the ??.

\(-8(t^2-6t+9)=-40-72\)

The reason we complete the square is found on the left side of the equals sign. We have, in the process of completing the square, formed a perfect square binomial that will serve as the h in our vertex (h, k) where h is the number of seconds it takes for the baseball to reach its max height of k, whatever k is. That's what we have to find out. Putting the left side into its simplified perfect square binomial and adding the numbers on the right gives us:

\(-8(t-3)^2=-112\)

For the last step, add over the -112 and set it back equal to f(t):

\(-8(t-3)^2+112=f(t)\) From that we determine that the vertex is (3, 112). The max height of this baseball was 112 feet...so no, it did not make it up to the height of 120 feet that Jimmy wanted for the baseball.

Answer:

Nonlinear

Step-by-step explanation:

Considering the definition of perpendicular line, the equation of the straight line passing through the point (0,-1) which is perpendicular to the line y=3/4x-3 is y= -4/3x -1.

A linear equation o line can be expressed in the form y = mx + b

where

Perpendicular lines are lines that intersect at right angles or 90° angles. If you multiply the slopes of two perpendicular lines, you get –1.

The line is y= 3/4x - 3. The line has a slope of  3/4.

If you multiply the slopes of two perpendicular lines, you get –1, you get:

3/4× slope perpendicular line= -1

slope perpendicular line= (-1)÷ (3/4)

slope perpendicular line= -4/3

The perpendicular line has a form of: y= -4/3x + b

The line passes through the point (0, -1). Replacing in the expression for perpendicular line:

-1= -4/3×0 + b

-1= 0 + b

-1= b

Finally, the equation of the perpendicular line is y= -4/3x -1 .

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Step-by-step explanation:

r - 18 = 27

r = 27 + 18

r = 45

...

Answer:

r=45

Step-by-step explanation:

r-18 =27

r=27 +18

r=45

45 - 18 =27

The equation of the tangent line at x=0 is y = x.

To find the equation of the tangent line at the given value of x, we need to find the derivative of the function y with respect to x and evaluate it at x=0.

Taking the derivative of y=∫[0 to x] sin(2t^2+π/2) dt using the Fundamental Theorem of Calculus, we get:

dy/dx = sin(2x^2+π/2)

Now we can evaluate this derivative at x=0:

dy/dx |x=0 = sin(2(0)^2+π/2)

        = sin(π/2)

        = 1

So, the slope of the tangent line at x=0 is 1.

To find the equation of the tangent line, we also need a point on the line. In this case, the point is (0, y(x=0)).

Substituting x=0 into the original function y=∫[0 to x] sin(2t^2+π/2) dt, we get:

y(x=0) = ∫[0 to 0] sin(2t^2+π/2) dt

      = 0

Therefore, the point on the tangent line is (0, 0).

Using the point-slope form of a linear equation, we can write the equation of the tangent line:

y - y1 = m(x - x1)

where m is the slope and (x1, y1) is a point on the line.

Plugging in the values, we have:

y - 0 = 1(x - 0)

Simplifying, we get:

y = x

So, the equation of the tangent line at x=0 is y = x.

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Answer:

D

\(x = \frac{11}{ \tan(30 \degree) } \\ x = 11 \sqrt{3} \)

\(y = \frac{11}{ \sin(30 \degree) } \\ y = 22\)

The period of the given trigonometric function is: 20.

The distance between the repetition of any function is called the period of the function. For a trigonometric function, the length of one complete cycle is called a period.

Sine and cosine functions start repeating the same pattern of y-axis values after every 2(pi). The period is defined as just the distance on the x-axis before the pattern repeats.

Now, looking at the trigonometric graph, we see that the x-interval for which the graph repeats itself is 20

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Answer:

i think b

Step-by-step explanation:

Answer:

\(c. \: {3}^{3} \)

Step-by-step explanation:

\( {3}^{3} \)

Answer:

21

Step-by-step explanation:

3n - 15 - 6 + 2n = 4n

3 n + 2n = 4n + 15 + 6

5 n - 4n = 15 + 6

n = 21

Answer:

 n = 21

Step-by-step explanation:

Use distributive rule: a(b + c) = a*b + a*c

3(n -5) - (6 - 2n) = 4n

3*n - 3*5 + 6*(-1) - 2n *(-1) = 4n

3n  - 15 - 6 + 2n = 4n             {add like term in LHS}

3n + 2n - 15 - 6 = 4n

            5n - 21  = 4n              {add 21 to both sides}

       5n -21 + 21 = 4n +21

                     5n = 4n + 21         {subtract 4n from both sides}

             5n - 4n = 4n -4n +21

   n = 21

Answer:

∠GHJ and ∠IHJ

Answer:

[-10, 10]

This is an absolute value problem and numbers within the brackets are always seen as positive. [-10] = 10   and [10] = 10

Step-by-step explanation:

neither even nor odd.

a) Sketch the function $f$Firstly, if $x < -3$ then $f(x) = 4-x$.This function starts from (4, 0) and goes downwards towards the negative infinity direction. Hence, the graph of $f(x) = 4 - x$ will be a line of negative slope passing through $(4,0)$.b) Show that $f$ is continuous everywhereFor proving that the function $f$ is continuous everywhere, we need to prove that the limit of $f(x)$ exists and is equal to $f(c)$, where $c$ is any arbitrary value of $x$; i.e.$$ \lim_{x\rightarrow c} f(x) = f(c) $$Since this is a linear function and all its powers are 1, the limit will exist at any point on the domain. And since the function is linear in nature, it will be continuous throughout its domain. Therefore, the function $f$ is continuous everywhere.c) Is the function $f$ even, odd, or neither?The function $f$ is neither odd nor even.The function $f$ is even if it satisfies $f(-x) = f(x)$.The function $f$ is odd if it satisfies $f(-x) = -f(x)$.To check if the function $f$ is odd, we will substitute $-x$ in place of $x$ in the function $f(x) = 4-x$ and check if $-f(x) = f(-x)$ holds or not.$$f(-x) = 4 - (-x) = 4 + x$$$$-f(x) = -4 + x$$$$f(-x) \neq -f(x)$$Therefore, the function $f$ is neither even nor odd.

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Answer:

Below

Step-by-step explanation:

The line L has the following equation:

● 2x - 3y = 5

Add -2x to both sides

● 2x - 3y -2x = 5 - 2x

● -3y = 5 - 2x

Multiply both sides by -1

● (-1) × -3y = (-1) × (5-2x)

● 3y = 2x - 5

Divide both sides by 3

● 3y/3 = (2x - 5)/3

● y = (2/3)x - 5/3

The line M is perpendicular to L

So the product of their slopes is -1

Let m be the slope of M

● m × (2/3) = -1

● m = -1 × (3/2)

● m = -3/2

So the equation of M is:

● y = (-3/2)x + b

b is the y-intercept

M passes through (2, -10)

Replace by the coordinates of this point

● -10 = (-3/2)×2 + b

● -10 = -3 + b

● b = -10 + 3

● b = -7

The equation of M is

● y = (-3/2)x -7

The statement '15 more than the sum of 5 and a number' is equivalent to the mathematical expression (5+n)+15.

Therefore the answer is (5+n)+15.

The statement "15 more than the sum of 5 and a number" is asking for an expression that represents the value that is 15 greater than the result of adding 5 and a number together. The mathematical way to express this is:

15 + (5 + n)

Where n is the number that we are adding to 5.

15 is being added to the sum of 5 and n. The parentheses around the 5 and n indicate that those two values are being added together before the 15 is added to them.

In other forms of representation

15+(5-n) or (5+n)+15 or (5-n) +15 or 15+5n does not convey the meaning you want it to convey as these forms does not represent "15 more than the sum of 5 and a number"

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The 95% confidence interval of the true mean is given as follows:

(0.977, 1.103).

The t-distribution is used when the standard deviation for the population is not known, and the bounds of the confidence interval are given according to the equation presented as follows:

\(\overline{x} \pm t\frac{s}{\sqrt{n}}\)

The variables of the equation are listed as follows:

The critical value, using a t-distribution calculator, for a two-tailed 95% confidence interval, with 35 - 1 = 34 df, is t = 2.0322.

The parameters for this problem are given as follows:

\(\overline{x} = 1.04, s = 0.18, n = 34\)

The lower bound of the interval is given as follows:

\(1.04 - 2.0322 \times \frac{0.18}{\sqrt{34}} = 0.977\)

The upper bound of the interval is given as follows:

\(1.04 + 2.0322 \times \frac{0.18}{\sqrt{34}} = 1.103\)

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Given data

*BE = 4x - 12

*DE = 2x + 8

At the point of intersection AC and BD, "x" is exactly split into halves.

Therefore

Substitute the values in the above expression as

Thus, the value of x equals to 10

The diameter of a standard nail that is 3 inches long is 0.15 feet.

In mathematics, an equation is a formula that expresses the equality of two expressions, by connecting them with the equals sign =.

The given equation is \(l=54d^{\frac{3}{2} }\), where d is the diameter (in inches) of the nail.

A standard nail that is 3 inches long.

Now, \(l=54\times(3)^{\frac{3}{2} }\)

\(3=54\times(d)^{\frac{3}{2} }\)

\((d)^{\frac{3}{2} }=\frac{3}{54}\)

\((d)^{\frac{3}{2} }=\frac{1}{18}\)

Raise 2/3 on both the sides of an equation

\((d)^{\frac{3}{2}\times\frac{2}{3} }=(\frac{1}{18})^{\frac{2}{3} }\)

d=0.15

Therefore, the diameter of a standard nail that is 3 inches long is 0.15 feet.

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Answer:

Choice D

Step-by-step explanation:

According to the graph, f(-8)=-8

Answer:

I'm confused by the question.

Step-by-step explanation:

Answer:

\(\huge \boxed{\mathrm{5^{3+2} \ \ \ \ 5^5 }}\)

Step-by-step explanation:

5³ × 25

25 can be written as a base of 5.

5³ × 5²

We need expressions with fewest number of bases possible.

Apply exponent rule : \(a^b \times a^c = a^{b+c}\)

\(5^{3+2}\)

Add exponents.

\(5^5\)

Answer:

The answer is easy its 53 times 2 and 52 times 2

Step-by-step explanation:

The number of minutes a scented candle lasts if it burns out sooner than 80% of all scented candles is 244 minutes.

When the distribution is normal, we use the z-score formula.

In a set with mean µ and standard deviation σ , the z-score of a measure X is given by:

Z = (X – µ) / σ

The Z-score shows how many standard deviations the measure is from the mean. After finding the Z-score, need to look at the z-score table and discover the p-value associated with the z-score. This p-value is the probability that the value of the measure is smaller than X, means, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.

So, in this case, given that:

µ = 249, σ = 20

The number of minutes a scented candle lasts if it burns out sooner than 80% of all scented candles:

100 – 80 = 20th percentile, which is X when Z has a p-value of 0.2. So, X when Z = –0.253.

Now, put all the values into the formula:

Z = (X – µ) / σ

–0.253 = (X – 249) / 20

X – 249 = –0.253 * 20

X = 244

Hence, the candle burns for 244 minutes.

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We want to write and solve a system of equations to model the given situation.

The answers are:

A)

y =  50 + 4*x

y = 17 + 7*x

B) after 11 weeks.

C) 94 subscribers.

First, we must find the two linear equations, we know that Robin has 50 subscribers and she gets another 4 per week.

Then for Robin, we can write:

y = R(x) = 50 + 4*x

The equation that models the number of subscribers that Robin has at week x.

Dimitri at the moment has 17 subscribers and wins 7 per week, then his equation is:

y = D(x) = 17 + 7*x

A) Then the system of equations is just:

y =  50 + 4*x

y = 17 + 7*x

B) Now we must solve the system.

Notice that in both equations we have y isolated, then we can write:

50 + 4*x = y = 17 + 7*x

50 + 4*x =17 + 7*x

Now we can solve this for x:

50 + 4*x =17 + 7*x

50 - 17 = 7*x - 4*x

33 = 3*x

33/3 = 11 = x

This means that at week 11 they will have the same number of subscribers.

C) To get this we just need to evaluate any one of the two linear equations in x = 11

D(11) = 17 + 7*11 = 94

Both of them will have 94 subscribers.

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Answer:

9s+11

Step-by-step explanation:

Combine like terms → (7s+2s and 2+9 = 9s and 11) and boom

Answer:

\(9s + 11\)

Step-by-step explanation:

First:

\(7s - 2s \\ = 9s\)

second:

\(9 + 2 \\ = 11\)

The probability that any one of the ways identified in problem 3 is: 0.03.

In statistical hypothesis testing, the probability of observing a particular test statistic or a more extreme one under the null hypothesis is called the p-value. A small p-value indicates that the observed result is unlikely to occur by chance alone, and thus provides evidence against the null hypothesis.

In this case, problem 3 is not specified, so it is not possible to calculate the p-value. However, the hint suggests using the second part of the binomial equation. This might refer to the formula for calculating the probability of obtaining k or more successes in n independent Bernoulli trials, each with probability p of success. This formula is:

P(X ≥ k) = ∑(k to n) (n choose i) p^i (1-p)^(n-i)

where X is the number of successes, n is the number of trials, p is the probability of success in each trial, (n choose i) is the binomial coefficient, and the summation is taken from k to n inclusive.

If the null hypothesis is true, the probability of success is equal to the significance level α, which is typically chosen to be small (e.g., 0.05 or 0.01). The value of k depends on the specific problem and the test being performed.

Using this formula, we can calculate the probability of observing k or more successes in n trials when the null hypothesis is true. If this probability is small (i.e., less than α), we reject the null hypothesis in favor of the alternative hypothesis.

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Answer:

The answer is E, 38.

Step-by-step explanation:

6×1/3 can be written as 19/3.

Use the reciprocal of 1/6, which is 6, and multiply 19/3 and 6.

6 and 3 can be simplified with 2.

So: 19 × 2, which is 38.

Step-by-step explanation:

please it my steps to work on paper whorksheet