Eliza Savage received a statement from her bank showing a checking account balance of $324.18 as of January 18. Her own checkbook shows a balance of $487.38 as of January 29. The bank returned all of the cancelled checks but three. The amounts of these three checks are $15.00, $77.49, and $124.28. How much did Eliza deposit in her account between January 18 and January 29? 

       A. $197.24   B. $379.97   C. $54.44   D. $201.12

Answer:

Helen can make 2 loaves of bread and 4 batches of muffins.

Step-by-step explanation:

Let x be the number of loaves of bread

Let y be the number of batches of muffins

As per the given requirement of flour, the equation becomes:

[tex]3.5x+2.5y=17[/tex]   .......(1)

As per the given requirement of sugar, the equation becomes:

[tex]0.75x+0.75y=4.5[/tex]  .....(2)

Multiplying equation (1) with 0.3 and subtracting (2) from (1)

[tex]1.05x+0.75y=5.1[/tex] now subtracting (2) from this we get

=> [tex]0.3x=0.6[/tex]

So, x = 2

And as [tex]3.5x+2.5y=17[/tex] ; so substituting x = 2 here we get

[tex]3.5(2)+2.5y=17[/tex]

[tex]7+2.5y=17[/tex]

[tex]2.5y=17-7[/tex]

[tex]2.5y=10[/tex]

So, y = 4

Hence, there will be 2 loaves of bread and 4 batches of muffins.

Answer:

His insurance company will pay for damages.

Step-by-step explanation:

An insurance is a form of contract that permits an individual to transfer the responsibilities of a financial loss to an insurance company. The company bears the risk of the financial loss. Small amount of money are collected from their clients and summed together to pay for losses that the client may encounter in the future. Insurance safeguards an individual and his property from losses, misfortune, hazards or theft. Covered losses are paid for by the insurance company thereby reducing the financial costs for the  individual.  Examples include auto insurance , health insurance, disability insurance, and life insurance.

Answer:

The equation that models the total fee for using this cab company

[tex]y=\$2.50+\$0.40\times x[/tex]

Step-by-step explanation:

Initial rate charged by company = $2.50

Amount charged for an each mile = $0.40

Let the miles cover during a ride = x

Total cost of ride can given as = y

The equation that models the total fee for using this cab company

[tex]y=\$2.50+\$0.40\times x[/tex]

The graphical interpretation equation in an image.

Answer:

622,080

Step-by-step explanation:

thanks me later

The equation for profit is income – cost:

Profit = Income – Cost

Let us say that x is the number of sold amount

Profit = 9 x – (25,000 + 4 x)

Profit = 5 x – 25,000

Breakeven point occurs when Profit = 0, hence:

5 x = 25,000

x = 5,000

The breakeven is when 5,000 people uses the income tax app

we know that

the perimeter of a polygon is the sum of the length sides

in this problem we have a triangle

so

the polygon has three sides

Let

[tex]A(-5,4)\\B(1,4)\\C(3,-4)[/tex]

the perimeter is equal to

[tex]P=AB+BC+AC[/tex]

The formula to calculate the distance between two points is equal to

[tex]d=\sqrt{(y2-y1)^{2}+(x2-x1)^{2}}[/tex]

Step 1

Find the distance AB

[tex]A(-5,4)\\B(1,4)[/tex]

substitutes the values in the formula

[tex]d=\sqrt{(4-4)^{2}+(1+5)^{2}}[/tex]

[tex]d=\sqrt{(0)^{2}+(6)^{2}}[/tex]

[tex]dAB=6\ units[/tex]

Step 2

Find the distance BC

[tex]B(1,4)\\C(3,-4)[/tex]

substitutes the values in the formula

[tex]d=\sqrt{(-4-4)^{2}+(3-1)^{2}}[/tex]

[tex]d=\sqrt{(-8)^{2}+(2)^{2}}[/tex]

[tex]d=\sqrt{68}[/tex]

[tex]dBC=8.25\ units[/tex]

Step 3

Find the distance AC

[tex]A(-5,4)\\C(3,-4)[/tex]

substitutes the values in the formula

[tex]d=\sqrt{(-4-4)^{2}+(3+5)^{2}}[/tex]

[tex]d=\sqrt{(-8)^{2}+(8)^{2}}[/tex]

[tex]d=\sqrt{128}[/tex]

[tex]dAC=11.31\ units[/tex]

Step 4

Find the perimeter

the perimeter is equal to

[tex]P=AB+BC+AC[/tex]

substitutes the values

[tex]P=6+8.25+11.31=25.56\ units=25.6\ units[/tex]

therefore

the answer is

[tex]25.6\ units[/tex]

Final answer:

To convert the equation 7x - 4y + 8 = 0 to slope-intercept form, solve for y to get y = (7/4)x + 2, with a slope of 7/4 and a y-intercept of 2.

Explanation:

To write the equation 7x − 4y + 8 = 0 in slope-intercept form (y = mx + b), where m is the slope and b is the y-intercept, we want to solve for y. The steps are as follows:

Thus, the equation of the line in slope-intercept form is y = (7/4)x + 2. Here, the slope is 7/4 and the y-intercept is 2.

Answer:

[tex]x=1[/tex]

Step-by-step explanation:

We have been given an equation [tex]\sqrt{x+3}+4=6[/tex]. We are asked to find the solution of our given equation.

[tex]\sqrt{x+3}+4-4=6-4[/tex]

[tex]\sqrt{x+3}=2[/tex]

Now, we will square both sides of our given equation.

[tex]x+3=2^2[/tex]

[tex]x+3=4[/tex]

[tex]x+3-3=4-3[/tex]

[tex]x=1[/tex]

To see whether [tex]x=1[/tex] is an extraneous solution or not, we will substitute [tex]x=1[/tex] in our given equation as:

[tex]\sqrt{1+3}+4=6[/tex]

[tex]\sqrt{4}+4=6[/tex]

[tex]2+4=6[/tex]

[tex]6=6[/tex]

Since both sides of our given equation are equal, therefore, [tex]x=1[/tex] is a solution for our given equation.

2.25 * 45 = 101.25 miles to work

101.25 / 25 = 4.05 gallons of gas

4.05 * 2.75 = $11.14 total cost of gas

Answer:  t represents the the number of seconds after rocket is released.

Step-by-step explanation:

Given: The height of a rocket a given number of seconds after it is released is modeled by [tex]h (t) = 6t^2 + 32t + 10[/tex].

Here h (height) is the dependent variable , which depends on the number of seconds after rocket is released (independent variable).

Since the independent variable in the function is t, then t must represents the the number of seconds after rocket is released.

The variable t represents the number of seconds that have passed since the rocket was released.

Here we know that the height of a rocket a given number of seconds after it is released is modeled by:

h(t) = 6*t^2 + 32*t + 10

So this is a function that relates height with time in seconds, we know that the function models the height, so we must have that:

[h(t)] is equivalent to height.

This means that the other variable, t, must be related to time in seconds.

Then we can conclude that the variable t represents the number of seconds after the rocket has been released.

If you want to learn more about motion equations, you can read:

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Answer:

1) Average velocity = 10/3 m/s

2) Instantaneous velocity = -2 m/s
   Speed = 2 m/s to the left

3) (0, 3) ∪ (6, 8]

4) Going faster: (3, 4.5) ∪ (6, 8]
   Slowing down: (0, 3) ∪ (4.5, 6)

5) Total distance = 35.67 m (nearest hundredth)

Step-by-step explanation:

The relationships between position (displacement), velocity and acceleration are:

[tex]\boxed{\boxed{\begin{array}{c}\textbf{POSITION (s)}\\\\\text{Differentiate} \downarrow\qquad\uparrow\text{Integrate}\\\\\textbf{VELOCITY (v)}\\\\\text{Differentiate}\downarrow\qquad\uparrow \text{Integrate}\\\\\textbf{ACCELERATION (a)}\end{array}}}[/tex]

Given a particle is moving with velocity v(t) = t² - 9t + 18, to find its position s(t) we can integrate v(t):

[tex]\begin{aligned}\displaystyle s(t)=\int v(t)\;\text{d}t&=\int(t^2-9t+18)\;\text{d}t\\\\&=\dfrac{t^{2+1}}{2+1}-\dfrac{9t^{1+1}}{1+1}+18t+C\\\\&=\dfrac{t^{3}}{3}-\dfrac{9t^{2}}{2}+18t+C\end{aligned}[/tex]

As s(0) = 1, then:

[tex]\begin{aligned}s(0)=\dfrac{(0)^{3}}{3}-\dfrac{9(0)^{2}}{2}+18(0)+C&=1\\0-0+0+C&=1\\C&=1\end{aligned}[/tex]

Therefore, the position function s(t) is:

[tex]\large\boxed{s(t)=\dfrac{t^3}{3}-\dfrac{9t^2}{2}+18t+1}[/tex]

Given a particle is moving with velocity v(t) = t² - 9t + 18, to find its acceleration a(t) we can differentiate v(t):

[tex]\begin{aligned}a(t)=\dfrac{\text{d}}{\text{d}t}[v(t)]&=2\cdot t^{2-1}-1\cdot9t^{1-1}+0\\&=2t-9\end{aligned}[/tex]

Therefore, the acceleration function a(t) is:

[tex]\large\boxed{a(t)=2t-9}[/tex]

[tex]\hrulefill[/tex]

To find the average velocity over the interval [0, 8], use the formula:

[tex]\textsf{Average Velocity}=\dfrac{s(t_2)-s(t_1)}{t_2-t_1}[/tex]

In this case:

Calculate the position at t₁ and t₂ by substituting t = 0 and t = 8 into s(t):

[tex]s(0)=\dfrac{(0)^3}{3}-\dfrac{9(0)^2}{2}+18(0)+1}=1[/tex]

[tex]s(8)=\dfrac{(8)^3}{3}-\dfrac{9(8)^2}{2}+18(8)+1}=\dfrac{83}{3}[/tex]

Therefore:

[tex]\textsf{Average Velocity}=\dfrac{s(8)-s(0)}{8-0}=\dfrac{\frac{83}{3}-1}{8}=\dfrac{10}{3}\; \sf m/s[/tex]

Therefore, the average velocity is 10/3 m/s.

[tex]\hrulefill[/tex]

To find the instantaneous velocity at t = 5 seconds, substitute t = 5 into v(t):

[tex]\begin{aligned}v(5)&=(5)^2-9(5)+18\\&=25-45+18\\&=-2\end{aligned}[/tex]

So, the instantaneous velocity at t = 5 seconds is -2 m/s.

Speed is a scalar quantity that measures how fast an object is moving regardless of its direction. Therefore, speed is the magnitude of velocity:

[tex]\textsf{Speed}=|v(5)|=|-2|=2\;\sf m/s[/tex]

Therefore, the speed at t = 5 is 2 m/s to the left.

[tex]\hrulefill[/tex]

The particle changes direction when v(t) = 0.

[tex]\begin{aligned}v(t)&=0\\\implies t^2-9t+18&=0\\t^2-6t-3t+18&=0\\t(t-6)-3(t-6)&=0\\(t-3)(t-6)&=0\\\\t-3&=0\implies t=3\\t-6&=0\implies t=6\end{aligned}[/tex]

Therefore, the particle changes direction at t = 3 and t = 6.

We know that the position of the particle at t = 0 is 1 meter right of zero. Therefore:

Therefore, the time intervals between 0 ≤ t ≤ 8 when the particle is moving right is:

[tex]\hrulefill[/tex]

When a(t) > 0:

[tex]\begin{aligned}a(t)& > 0\\2t-9& > 0\\2t& > 9\\t& > \dfrac{9}{2}\\t& > 4.5\; \sf s\end{aligned}[/tex]

When a(t) < 0:

[tex]\begin{aligned}a(t)& < 0\\2t-9& < 0\\2t& < 9\\t& < \dfrac{9}{2}\\t& < 4.5\; \sf s\end{aligned}[/tex]

Therefore:

(Refer to the attachment).

If velocity and acceleration have the same sign, it means the object is speeding up.

If velocity and acceleration have opposite signs, it means the object is slowing down.

Therefore, the time intervals when the particle is going faster and slowing down are:

[tex]\hrulefill[/tex]

To find the total distance the particle has traveled between 0 and 8 seconds, we need to consider the distance traveled between the intervals when it changes direction.

To do this, find the position of the particle at t = 0, t = 3, t = 6 and t = 8.

[tex]s(0)=\dfrac{(0)^3}{3}-\dfrac{9(0)^2}{2}+18(0)+1=1[/tex]

[tex]s(3)=\dfrac{(3)^3}{3}-\dfrac{9(3)^2}{2}+18(3)+1=23.5[/tex]

[tex]s(6)=\dfrac{(6)^3}{3}-\dfrac{9(6)^2}{2}+18(6)+1=19[/tex]

[tex]s(8)=\dfrac{(8)^3}{3}-\dfrac{9(8)^2}{2}+18(8)+1=\dfrac{83}{3}\approx27.67[/tex]

Therefore, in the interval 0 ≤ t < 3, the particle travels:

[tex]|s(3)-s(0)|=|23.5-1|=22.5\; \sf meters\;(to\;the\;right)[/tex]

In the interval  3 < t < 6, it travels:

[tex]|s(6)-s(3)|=|19-23.5|=4.5\; \sf meters\;(to\;the\;left)[/tex]

In the interval 6 < t ≤ 8, it travels:

[tex]|s(8)-s(6)|=|27.67-19|=8.67\; \sf meters\;(to\;the\;right)[/tex]

So the total distance the particle has traveled between 0 and 8 seconds is:

[tex]\textsf{Total distance}=22.5+4.5+8.67=35.67\; \sf meters[/tex]

To prove that (x-s-t) is a factor of the polynomial $x^3 - s^3 - t^3 -3st(s+t)$, we applied the factor theorem which states that (x-c) will be a factor of a polynomial if f(c) equals zero. By substituting x with (s+t) into the polynomial, we got a value of zero, confirming that (x-s-t) is indeed a factor.

To prove that (x-s-t) is a factor of $x^3 - s^3 -t^3 -3st(s+t)$, we can use the factor theorem. According to the factor theorem, a polynomial f(x) has a factor (x-c) if and only if f(c) equals zero.

Given the polynomial $x^3 - s^3 - t^3 -3st(s+t)$, we substitute (x = s + t) into the polynomial, thus:

$f(s + t) = (s + t)^3 -s^3 -t^3 - 3st(s + t)$.

After simplifying the equation, we obtain:

$s^3 + 3s^2t +3st^2  + t^3 - s^3 - t^3 - 3st^2 - 3s^2t$.

When we cancel out the like terms, the result is 0. Therefore,

$(x - s - t)$ is a factor of the given polynomial $x^3 - s^3 -t^3 -3st(s+t)$. This proves our result according to the Factor theorem.

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The required polynomial function is x⁴ - 67x² + 1450x - 4984 = 0 with 4 degrees with real coefficients.

A polynomial is defined as a mathematical expression that has a minimum of two terms containing variables or numbers. A polynomial can have more than one term.

The zeros are given in the question as 4, -14, and 5 + 8i

The required polynomial function of minimum degree with real coefficients whose zeros include those listed above.

For the zero 4, you can write (x-4)

For the zero -14, you can write (x+14)

For the zero 5+8i since it is complex it will be accompanied by its conjugate 5-8i

So, you can write (x-(5+8i) and (x-(5-8i)) =(x²-10x+89)

(x - 4)(x + 14)(x² - 10x + 89)

Expanding the expression, we get

x⁴ - 67x² + 1450x - 4984 = 0

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we know that

Vertical angles are a pair of opposite and congruent angles formed by intersecting lines

In this problem

m∠JNM=m∠KNL -------> by vertical angles

so

[tex](4x+6)\°=(7x-21)\°[/tex]

Solve for x

[tex]7x-4x=6+21\\3x=27\\x=9\°[/tex]

Find the value of m∠JNM

m∠JNM=[tex](4x+6)\°[/tex]

substitute the value of x

m∠JNM=[tex](4*9+6)\°[/tex]

m∠JNM=[tex]42\°[/tex]

therefore

the answer is

m∠JNM=[tex]42\°[/tex]

The only way I can think of to solve this problem is to assume normal distribution.

Since the total weight excess 5511, hence the weight per passenger is at least:

x = 5511 / 27 = 204.1 pounds

Solve for the z score:

z = (x – u) / s

z = (204.1 – 189.7) / 41.4

z = 0.35

From the standard probability tables, the P value using right tailed test is:

P = 0.3632

Answer:

-162

Step-by-step explanation:

Integration by substitution is a technique in calculus where a change of variables is made to simplify the integral by expressing it in terms of a new variable, making the integration easier to manage.

To evaluate the following integral, use the method of substitution:

[tex]\displaystyle \int_{-1}^0 (2x^4 + 8x)^3 (4x^3 + 4) \;\text{d}x[/tex]

Let u = 2x⁴ + 8x.

Differentiate u with respect to x using the power rule for differentiation by multiplying each term by its exponent and then subtracting 1 from the exponent:

[tex]\dfrac{\text{d}u}{\text{d}x}=4 \cdot 2x^{4-1}+1\cdot 8 x^{1-1}[/tex]

[tex]\dfrac{\text{d}u}{\text{d}x}=8x^{3}+8[/tex]

Rewrite it so that dx is on its own:

[tex]\text{d}u=8x^{3}+8\;\text{d}x[/tex]

[tex]\text{d}x=\dfrac{1}{8x^{3}+8}\;\text{d}u[/tex]

Change the limits of integration from x to u:

[tex]\begin{aligned}x=-1 \implies u&=2(-1)^4 + 8(-1)\\&=2(1)-8\\&=2-8\\&=-6\end{aligned}[/tex]

[tex]\begin{aligned}x=0 \implies u&=2(0)^4 + 8(0)\\&=2(0)-0\\&=0-0\\&=0\end{aligned}[/tex]

Rewrite the integral in terms of u:

[tex]\begin{aligned}\displaystyle \int_{-1}^0 (2x^4 + 8x)^3 (4x^3 + 4) \;\text{d}x&=\int_{-6}^0 u^3 (4x^3 + 4) \cdot \dfrac{1}{8x^{3}+8}\;\text{d}u\\\\&=\int_{-6}^0 u^3 (4x^3 + 4) \cdot \dfrac{1}{2(4x^{3}+4)}\;\text{d}u\\\\&=\int_{-6}^0\dfrac{u^3}{2} \;\text{d}u\end{aligned}[/tex]

Integrate with respect to u using the power rule for integration by adding 1 to the exponent of each term and then dividing by the new exponent:

[tex]\begin{aligned}\displaystyle \int_{-6}^0\dfrac{u^3}{2} &=\left[\dfrac{u^{3+1}}{2 \cdot (3+1)}\right]^0_{-6}\\\\&=\left[\dfrac{u^{4}}{8}\right]^0_{-6}\\\\&=\dfrac{(0)^4}{8}-\dfrac{(-6)^4}{8}\\\\&=0-\dfrac{1296}{8}\\\\&=-162\end{aligned}[/tex]

Therefore, the value of the given integral is -162.

Answer:

It must be greater than 1/2XY.

Step-by-step explanation:

We draw an arc from point X below the arc that passes through X and Y.  Keeping our compass the same width, we will draw another arc from point Y below, intersecting the first arc.

If the width of the compass is not set to more than 1/2XY, then the two arcs will not intersect and we will not complete our construction.

Perpendicular lines are lines that meet at 90 degrees.

The true statement about the width of the compass is that: (d) It must be greater than 1/2XY.

From the question, we understand that he has drawn arc XY already.

The next step is to draw an arc less than the width of XY, but greater than half width XY.

This will ensure that the arcs bisect one another.

Hence, the true option is (d).

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