omari buys a computer for $1099. He makes a down payment of 20%. His monthly payments for the computer are $144. How many months will it take omari to finish paying off the computer

Therefore, the rate of change, in cm per minute, of the height when the height is 6 cm is approximately -6 cm/min.

Given,The width of the box = 10 cm Length of the box = 17 cmThe volume of the box = 527 cubic cm/minWe need to find the rate of change, in cm per minute, of the height when the height is 6 cm.We know that the volume of the box is given as:V = l × w × h where, l, w and h are length, width, and height of the box respectively.It is given that the width and length are being held constant.

Therefore, we can write the volume of the box as

:V = constant × h Differentiating both sides with respect to time t, we get:dV/dt = constant × dh/dtNow, it is given that the volume of the box is decreasing at a rate of 527 cubic cm per minute.

Therefore, dV/dt = -527.Substituting the given values in the above equation, we get:

527 = constant × dh/dt

We need to find dh/dt when h = 6 cm.To find constant, we can use the given values of length, width and height.Substituting these values in the formula for the volume of the box, we get:

V = l × w × hV = 17 × 10 × hV = 170h

We know that the volume of the box is given as:V = constant × hSubstituting the value of V and h, we get:

527 = constant × 6 cm

constant = 87.83 cm/minSubstituting the values of constant and h in the equation, we get

-527 = 87.83 × dh/dtdh/dt = -6.0029 ≈ -6 cm/min

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Answer:

\(y=-x+1\)

Step-by-step explanation:

It helps to write the equation in slope-intercept formula to find the slope of an equation in the form: \(y=mx+b\) where "m" is the slope of the equation. We can take the equation given: \(-7x-7y=7\) and solve for "y" to get the equation in slope-intercept form:

\(-7x-7y=7\)

add 7x to both sides:

\(-7y=7x+7\)

Divide both sides by -7

\(y=-x-1\)

Now in this form we can tell that the coefficient of "x" (the m value) is our slope, which is -1. We need this slope to determine a parallel line as parallel lines share the same slope but different y-intercepts. So a general equation for a parallel line would be:

\(y=-x+b\text{ where b }\ne -1\)

We're given the point (-1, 2) and we can use it to solve for that "b" value.

We plug in -1 as x and 2 as y

\(2=-1(-1)+b\implies 2=1+b\implies 1=b\)

Now we just plug this into the general equation to get: \(y=-x+1\)

Multiply 15 and 6.8. So speed * time = distance

So the answer is 102

The amount of the area of the home used and the total area of the second property are 26.25 acres and 20.625 acres respectively.

The amount of land to be used for a home is the difference between the total land area and the area to be used for land :

Land Area of second property = 0.78 times the land ares

Therefore, the total area of the second property is 20.625 acres.

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Answer: -2x

Step-by-step explanation:

4x+(-6x)

When there is a + in front of an expression in a parentheses, the expression remains the same.

4x-6x

Collect like terms

-2x

Answer: what do you mean

Step-by-step explanation:

Answer:

No, the Normal/large sample condition is not met. A confidence interval assumes that the underlying population follows a normal distribution and that the sample size should be at least 30. Since the sample size in this case is only 10, the Normal/Large Sample condition is not met and the conditions for constructing a confidence interval are not met.

Answer:

3/10

Step-by-step explanation:

There are a total of three people. 1/2 of the blueberry pie plus 2/5 of the apple pie is equal to 9/10 of a whole pie. Divide that by 3 and each person gets 3/10 of pie.

\(f(x)=2(3)^{x+1} \\\\[-0.35em] ~\dotfill\\\\ f(2)=2(3)^{(2)+1}\implies f(2)=2(3)^3\implies f(2)=2(3^3) \\\\\\ f(2)=2(27)\implies f(2)=54\)

if we notice the tickmarks on the triangle, we can see the all sides are equal, namely is an equilateral triangle, and if all sides are equal, then all interior angles are equal as well.

Let's recall that the sum of all interior angles in a triangle is 180°, now if we divide that by 3, that gives us 60, namely each angle in the equilateral triangle is 60°, that means

\(10x=60\implies x=\cfrac{60}{10}\implies \boxed{x=6} ~\hfill 12y=60\implies y=\cfrac{60}{12}\implies \boxed{y=5}\)

Step-by-step explanation:

we can make it as a ratio

90/100=27/total Q

total Q= (27*100)/90=30

So wrong questions=30-27=3

hope this helps!

Answer:

a=55°

b=123°

c=55°

d=123°

Answer:

She spend $280 a month when she goes out to eat 8 times a month.

She will save $105 a month if she cuts back to 5 times a month.

Step-by-step explanation:

35 x 8= 280

35 x 5  = 175

280 - 175 = 105

Answer:

8 * $35 per meal = $280

$280 - (5 * $35)

= $280 - ($175)

= $105

Step-by-step explanation:

Answer:

36 times 8 =  288

Let's start by using the formula for the height of an object thrown upward:

h(t) = -0.5gt^2 + v0t + h0

where:

h(t) is the height of the object at time t

g is the acceleration due to gravity (9.8 m/s^2)

v0 is the initial velocity (21 m/s)

h0 is the initial height (22 m)

We want to find the time t when the rock is 9 meters from ground level. So, we can set h(t) equal to 9 meters and solve for t:

9 = -0.5(9.8)t^2 + 21t + 22

Rearranging this equation, we get:

0.5(9.8)t^2 - 21t - 13 = 0

Using the quadratic formula, we can solve for t:

t = [21 ± sqrt(21^2 - 4(0.5)(9.8)(-13))] / (2(0.5)(9.8))

t ≈ 2.41 seconds or t ≈ 4.01 seconds

We want the time when the rock is 9 meters from ground level on the way down, so we need to choose the larger value of t. Therefore, the rock will be 9 meters from ground level about 4.01 seconds after it was thrown upward.

The y-coordinate of -3f(x-1) when x = 0 is -63

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

The table of values

So, we have

-3f(x - 1)

When x = 0, we have

y = -3f(0 - 1)

This gives

y = -3f(-1)

From the table, we have

y = -3 * 21

Evaluate

y = -63

Hence, the y-coordinate is -63

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Answer:

23% increase

Step-by-step explanation:

13 - 10 = 3

3/13 = 0.2307 = 23%

Hope that helped!!! k

The solution to the inequality f(x²-2) < f(7x-8) over D₁ = (-∞, 2) is:

-∞ < x < 1 or 1 < x < 6 or 6 < x < 2

Given the inequality,

    f(x²-2) < f(7x-8) over D₁ = (-∞, 2)

We need to find the values of x that satisfy this inequality.

Since we know that f is increasing over its domain, we can compare the values inside the function to determine the values of x that satisfy the inequality.

First, we can find the values of x that make the expressions inside the function equal:

x² - 2 = 7x - 8

Simplifying, we get:

x² - 7x + 6 = 0

Factoring, we get:

(x - 6)(x - 1) = 0

So the values of x that make the expressions inside the function equal are x = 6 and x = 1.

We can use these values to divide the domain (-∞, 2) into three intervals:

-∞ < x < 1, 1 < x < 6, and 6 < x < 2.

We can choose a test point in each interval and evaluate

f(x² - 2) and f(7x - 8) at that point. If f(x² - 2) < f(7x - 8) for that test point, then the inequality holds for that interval. Otherwise, it does not.

Let's choose -1, 3, and 7 as our test points.

When x = -1, we have:

f((-1)² - 2) = f(-1) < f(7(-1) - 8) = f(-15)

Since f is increasing, we know that f(-1) < f(-15), so the inequality holds for -∞ < x < 1.

When x = 3, we have:

f((3)² - 2) = f(7) < f(7(3) - 8) = f(13)

Since f is increasing, we know that f(7) < f(13), so the inequality holds for 1 < x < 6.

When x = 7, we have:

f((7)² - 2) = f(47) < f(7(7) - 8) = f(41)

Since f is increasing, we know that f(47) < f(41), so the inequality holds for 6 < x < 2.

Therefore, the solution to the inequality f(x²-2) < f(7x-8) over D₁ = (-∞, 2) is:

-∞ < x < 1 or 1 < x < 6 or 6 < x < 2

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Answer:

There are no two numbers whose product is 52 and whose sum is 11.

Step-by-step explanation:

give the 1st number is x and the 2nd number is y, then

x + y = 11 and xy = 52

x + y = 11 => y = 11 - x

x(11 - x) = 52

11x - x^2 = 52

=> x^2 - 11x + 52 = 0

Using quadratic formula: ax^2 + bx + c = 0

with a = 1, b = -11, c = 52

=> x = [-b ± √(b^2 - 4ac)]/2a

=> x = [-(-11) ± √((-11)^2 - 4x1x52)]/2x1

=> x = [11 ± √(121 - 208)]/2

=> x = [11 ± √(-87)]/2

Since the square root of a negative number is not a real number, there are no real solutions to this equation. Therefore, there are no two numbers whose product is 52 and whose sum is 11.

The prove that the angle ABCD is said to be a parallelogram that shows both pairs of opposite sides as parallel figure is given below.

The four points in the shape above are : A, B, C, D.

Where

A = (-2,-4)

B = (1,2)

C = (2,10)

D = (-1,4)

We place or sit vector AB with vector DC and vector AD  with vector BC

and so we find and place their coordinates.

vector AB (1-(-2), 2-(-4))

vector DC (2-(-1),10-4)

vector AD (-1-(-2), 4-(-4))

vector BC (2-1,10-2)

So we obtained:

vector AB (3,6)

vector DC (3,6)

vector AD (1,8)

vector BC  (1,8)

Next step is to calculate for the lengths :

AB=   \(\sqrt{3^{2} + 6^{2} }\)  DC= \(\sqrt{3^{2} + 6^{2} }\)

Thus, AB = DC

AD = \(\sqrt{1^{2} + 8^{2} }\)     BC =\(\sqrt{1^{2} + 8^{2} }\)

Hence one can say that  AD is equal to  BC.

Therefore, angle ABCD IS known to be a parallelogram .

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Answer: I'm pretty sure its 14.

Step-by-step explanation: 14 + 7 - 9 - 4 + 8 - 2 = 14

From the sampling distribution, the correct answer is: Both the center will remain the same, but the spread will decrease.

The center of the sampling distribution will remain the same, which is the expected proportion of even numbers showing on a single roll of the die, which is 1/2 or 0.5. This is because the probability of getting an even number on a single roll of the die does not change with the number of rolls in the experiment.

However, the spread of the sampling distribution will decrease as the number of rolls increases. This is because the larger the sample size, the more precise our estimate of the proportion of even numbers showing on each roll of the die will be. With more rolls, we will have a better idea of the true proportion of even numbers that the die produces.

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Direct distance from the base of the Space Needle to Kasie's house = 1429 feet.

The angle of depression is the angle between the horizontal line and the observation of the object from the horizontal line. It is basically used to get the distance of the two objects where the angles and an object's distance from the ground are known to us.

Given,

Height of the observation deck AB = 520 feet

Angle of depression = 70°

Distance of the Space needle base to house BC = ?

By the figure,

tan70° = AB/BC

BC = tan70°(AB)

BC = 2.7475(520)

BC = 1428.7 feet

Distance of the Space needle base to house to nearest foot = 1429 feet

Hence, 1429 feet is the distance between base of the Space Needle to Kasie's house.

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Answer:

a

Step-by-step explanation:

The midline is at y=2.

Eliminate c, d, e

Also, since there is no horizontal shift amongst the remaining options, we know that since y=2 when x=0, this means it must be a sine curve.

This means the answer is a.

The number of minutes for 20 bacteria be left is 439minutes. The decay constant is 0.0081

An exponential function is a mathematical function, which is used in many real-world situations. It is mainly used to find the exponential decay or exponential growth or to compute investments, model populations and so on.

The No of bacteria left at a particular time t is given as N(t)= Noe^-kt

where No= initial number of bacteria

k= decay constant and t = time

after 13 minutes

630= 700e^-13k

divide both sides by 700

630/700= e^-13k

0.9= e^-13k

ln0.9= -13k

k= ln0.9/-13 = -0.1054/-13 = 0.0081

time for 20 bacteria to be left =

20= 700e^-0.0081t

= 20/700=e^-0.0081t

0.0286= e^-0.0081t

ln0.0286= -0.0081t

-3.554= -0.0081t

divide both sides by -0.0081

t= -3.554/-0.0081= 439 minutes ( nearest minutes)

therefore the time for the bacteria to be left is 439minutes

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Answer:

Dependent variable: time(months) or \(t\)

Independent variable: 6

Step-by-step explanation:

\(h=24+6t\)

(h=height)

Answer:

The following are the solution to the given points:

Step-by-step explanation:

Given value:

\(1) \sum ^{\infty}_{k = 1} \frac{1}{k+1} - \frac{1}{k+2}\\\\2) \sum ^{\infty}_{k = 1} \frac{1}{(k+6)(k+7)}\)

Solve point 1 that is \(\sum ^{\infty}_{k = 1} \frac{1}{k+1} - \frac{1}{k+2}\\\\\):

when,

\(k= 1 \to s_1 = \frac{1}{1+1} - \frac{1}{1+2}\\\\\)

                  \(= \frac{1}{2} - \frac{1}{3}\\\\\)

\(k= 2 \to s_2 = \frac{1}{2+1} - \frac{1}{2+2}\\\\\)

                  \(= \frac{1}{3} - \frac{1}{4}\\\\\)

\(k= 3 \to s_3 = \frac{1}{3+1} - \frac{1}{3+2}\\\\\)

                  \(= \frac{1}{4} - \frac{1}{5}\\\\\)

\(k= n^ \to s_n = \frac{1}{n+1} - \frac{1}{n+2}\\\\\)

Calculate the sum \((S=s_1+s_2+s_3+......+s_n)\)

\(S=\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+\frac{1}{4}-\frac{1}{5}+.....\frac{1}{n+1}-\frac{1}{n+2}\\\\\)

   \(=\frac{1}{2}-\frac{1}{5}+\frac{1}{n+1}-\frac{1}{n+2}\\\\\)

When \(s_n \ \ dt_{n \to 0}\)

\(=\frac{1}{2}-\frac{1}{5}+\frac{1}{0+1}-\frac{1}{0+2}\\\\=\frac{1}{2}-\frac{1}{5}+\frac{1}{1}-\frac{1}{2}\\\\= 1 -\frac{1}{5}\\\\= \frac{5-1}{5}\\\\= \frac{4}{5}\\\\\)

\(\boxed{\text{In point 1:} \sum ^{\infty}_{k = 1} \frac{1}{k+1} - \frac{1}{k+2} =\frac{4}{5}}\)

In point 2: \(\sum ^{\infty}_{k = 1} \frac{1}{(k+6)(k+7)}\)

when,

\(k= 1 \to s_1 = \frac{1}{(1+6)(1+7)}\\\\\)

                  \(= \frac{1}{7 \times 8}\\\\= \frac{1}{56}\)

\(k= 2 \to s_1 = \frac{1}{(2+6)(2+7)}\\\\\)

                  \(= \frac{1}{8 \times 9}\\\\= \frac{1}{72}\)

\(k= 3 \to s_1 = \frac{1}{(3+6)(3+7)}\\\\\)

                  \(= \frac{1}{9 \times 10} \\\\ = \frac{1}{90}\\\\\)

\(k= n^ \to s_n = \frac{1}{(n+6)(n+7)}\\\\\)

calculate the sum:\(S= s_1+s_2+s_3+s_n\\\)

\(S= \frac{1}{56}+\frac{1}{72}+\frac{1}{90}....+\frac{1}{(n+6)(n+7)}\\\\\)

when \(s_n \ \ dt_{n \to 0}\)

\(S= \frac{1}{56}+\frac{1}{72}+\frac{1}{90}....+\frac{1}{(0+6)(0+7)}\\\\= \frac{1}{56}+\frac{1}{72}+\frac{1}{90}....+\frac{1}{6 \times 7}\\\\= \frac{1}{56}+\frac{1}{72}+\frac{1}{90}+\frac{1}{42}\\\\=\frac{45+35+28+60}{2520}\\\\=\frac{168}{2520}\\\\=0.066\)

\(\boxed{\text{In point 2:} \sum ^{\infty}_{k = 1} \frac{1}{(n+6)(n+7)} = 0.066}\)

Answer:

Step-by-step explanation:

Remark.

I take it that this is a calculus question question.

Expand c(x)

c(x) = 0.45 + 0.2x - 0.2        Combine

c(x) = 0.25 + 0.2x/dx

c(x) =  0.2