Acorn falls from a tree "h=98-18t^(2)" (height depends on time)

a) When "t=2 seconds," find "h"
____ft

b) Find "t" when the acorn hits the ground. (to nearest tenth)
____seconds

The formula for determining the z score is expressed as

z = (data value - mean)/standard deviation

a) data value = 110

mean = 87

standard deviation = 11

z = (110 - 87)/11

z = 2.09

b) data value = 110

mean = 80

standard deviation = 11

z = (80 - 87)/11

z = - 0.64

The function that gives the total expenditures x years after 2000 is: f(x) = 9.28x + 87.27. The total expenditures in 2015 will be $226.47 billion.

Given that the total expenditures in a country (in billions of dollars) are increasing at a rate of

f(x) = 9.28x + 87.27,

where x = 0 corresponds to the year 2000.

Total expenditures were $1590.8 billion in 2002.

We need to find the function that gives the total expenditures x years after 2000.f(x) = 9.28x + 87.27 is a linear function.

We know that y = mx + b, where m is the slope and b is the y-intercept.

Using this, we can write the equation for total expenditure as:

f(x) = 9.28x + 87.27

When x = 0, f(x) = 87.27, which is the expenditure in 2000.

Therefore, the function that gives the total expenditures x years after 2000 is:

f(x) = 9.28x + 87.27

We need to find the total expenditures in 2015.2015 is 15 years after 2000.

So, x = 15.

To find the total expenditure in 2015, substitute x = 15 in the function f(x).

f(x) = 9.28x + 87.27f(15) = 9.28(15) + 87.27= 139.20 + 87.27= 226.47

So, the total expenditures in 2015 will be $226.47 billion.

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Answer:

Given, hope it helps!

Step-by-step explanation:

Perimeter= 510 feet

Perimeter is the sum of sides so..

16x + 11x + 24x = 510

51x = 510

x = 510/51 = 10

(10*24), (10*11), (10*16)

So the sides are 160ft 110ft and 240ft

Area is equal to √s(s-a)(s-b)(s-c)

where s is the semiperimeter= 510/2 = 255

and a, b and c are the sides

area =

√ 255(255-240)(255-110)(255-160)

= √ 255*15*145*95

= √ 52,689,375

= 7258.74 feet ^2

Answer:

A=7258.74472

Step-by-step explanation:

Multiply the side ratios by x

Add them together to get the perimeter

11x+16x+24x = 510

51 x =510

x = 10

The sides are 110, 160 240

We have to use herons formula

A = sqrt( p (p-a) (p-b)(p-c))  where p is the perimeter/2 and a,b,c are the side lengths

A = sqrt( 510/2 (510/2-110) (510/2-160)(510/2-240))

A = sqrt( 255 (145) (95)(15))

A = sqrt(52689375)

A=7258.74472

The only solution is a=b=c=d=0, which implies that the subspaces W1 and W2 are orthogonal. we have: α = -3 + 2d, β = -2 and c = 1 - 2d, We can choose d=0.

(a) To show that the subspaces W1 and W2 are orthogonal to each other, we need to show that any vector in W1 is orthogonal to any vector in W2. Since W1 is spanned by V1 and V2, any vector in W1 can be written as a linear combination of V1 and V2:

aV1 + bV2

Similarly, any vector in W2 can be written as a linear combination of V3 and V4:

cV3 + dV4

To show that these two subspaces are orthogonal, we need to show that the dot product of any vector in W1 with any vector in W2 is zero. Thus:

(aV1 + bV2)·(cV3 + dV4) = ac(V1·V3) + ad(V1·V4) + bc(V2·V3) + bd(V2·V4)

Calculating the dot products, we have:

V1·V3 = 2(0) + 2(1) + 1(3) = 7

V1·V4 = 2(2) + 2(6) + 1(4) = 20

V2·V3 = 6(0) + 1(1) + 3(3) = 10

V2·V4 = 6(2) + 1(0) + 3(4) = 24

Substituting these values into the dot product expression, we get:

(aV1 + bV2)·(cV3 + dV4) = 7ac + 20ad + 10bc + 24bd

Since we want this expression to be zero for any choice of a, b, c, and d, we can set up a system of equations:

7ac + 20ad + 10bc + 24bd = 0

where a, b, c, and d are arbitrary constants.

Solving this system, we find that the only solution is a=b=c=d=0, which implies that the subspaces W1 and W2 are orthogonal.

(b) To write the vector y = [2 3 4] as a sum of a vector in W1 and a vector in W2, we need to find scalars α and β such that:

αV1 + βV2 = [2 3 4] - (cV3 + dV4)

for some constants c and d. Rearranging, we have:

αV1 + βV2 + cV3 + dV4 = [2 3 4]

We can solve for α, β, c, and d by setting up a system of linear equations using the coefficients of the vectors:

α(0 1) + β(1 2) + c(1 3) + d(2 0) = (2 3 4)

This system of equations can be written as:

α + β + c + 2d = 2

α + 2β + 3c = 3

c = 4 - 2α - 3β - 2d

We can solve for α and β in the first two equations:

α = 2 - β - c - 2d

β = 3 - 3c

Substituting these into the third equation, we get:

c = 1 - 2d

Thus, we have:

α = -3 + 2d

β = -2

c = 1 - 2d

We can choose d=0, which implies that c

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Answer:

It's around 459. So 460 if need to round

Step-by-step explanation:

So, 40 randomly chosen people do not represent  the whole school, but using the ratio 27:40 you are given in the equation, you can divide the number of students (680) by the surveyed students (40) to get 17. What this means is there is 17 groups of 40 in the school, so to distribute the amount of people who are in a after-school activity, you must multiply 17 x 27 to get the assumption of about 459 kids. Hopefully you understand =)

answer:

i believe the answer is "a"

good luck :) hopefully, this helps

have a great day !!

The answer are: a. Total outflows: $2,007,901, b. Total inflows: $827,080, c. Net present value: $824,179, d. Should the old issue be refunded with new debt? Yes

To determine whether the old bond issue should be refunded with new debt, we need to calculate the present value of total outflows, the present value of total inflows, and the net present value (NPV). Let's calculate each of these values step by step: Calculate the present value of total outflows. The total outflows consist of the call premium, underwriting cost on the old issue, and underwriting cost on the new issue. Since these costs are one-time payments, we can calculate their present value using the formula: PV = Cash Flow / (1 + r)^t, where PV is the present value, Cash Flow is the cash payment, r is the discount rate, and t is the time period.

Call premium on the old issue: PV_call = (7% of $22 million) / (1 + 0.1)^16, Underwriting cost on the old issue: PV_underwriting_old = $530,000 / (1 + 0.1)^16, Underwriting cost on the new issue: PV_underwriting_new = $680,000 / (1 + 0.1)^16. Total present value of outflows: PV_outflows = PV_call + PV_underwriting_old + PV_underwriting_new. Calculate the present value of total inflows. The total inflows consist of the interest savings and the tax savings resulting from the interest expense deduction. Since these cash flows occur annually, we can calculate their present value using the formula: PV = CF * [1 - (1 + r)^(-t)] / r, where CF is the cash flow, r is the discount rate, and t is the time period.

Interest savings: CF_interest = (12% - 10%) * $22 million, Tax savings: CF_tax = (40% * interest expense * tax rate) * [1 - (1 + r)^(-t)] / r. Total present value of inflows: PV_inflows = CF_interest + CF_tax.  Calculate the net present value (NPV). NPV = PV_inflows - PV_outflows Determine whether the old issue should be refunded with new debt. If NPV is positive, it indicates that the present value of inflows exceeds the present value of outflows, meaning the company would benefit from refunding the old issue with new debt. If NPV is negative, it suggests that the company should not proceed with the refunding.

Now let's calculate these values: PV_call = (0.07 * $22,000,000) / (1 + 0.1)^16, PV_underwriting_old = $530,000 / (1 + 0.1)^16, PV_underwriting_new = $680,000 / (1 + 0.1)^16, PV_outflows = PV_call + PV_underwriting_old + PV_underwriting_new. CF_interest = (0.12 - 0.1) * $22,000,000, CF_tax = (0.4 * interest expense * 0.4) * [1 - (1 + 0.1)^(-16)] / 0.1, PV_inflows = CF_interest + CF_tax. NPV = PV_inflows - PV_outflows.  If NPV is positive, the old issue should be refunded with new debt. If NPV is negative, it should not.

Performing the calculations (rounded to the nearest whole dollar): PV_call ≈ $1,708,085, PV_underwriting_old ≈ $130,892, PV_underwriting_new ≈ $168,924, PV_outflows ≈ $2,007,901,

CF_interest ≈ $440,000, CF_tax ≈ $387,080, PV_inflows ≈ $827,080.  NPV ≈ $824,179.  Since NPV is positive ($824,179), the net present value suggests that the old bond issue should be refunded with new debt.

Therefore, the answers are:

a. Total outflows: $2,007,901

b. Total inflows: $827,080

c. Net present value: $824,179

d. Should the old issue be refunded with new debt? Yes

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Answer:

the answer is y=6x-6

Step-by-step explanation:

hope this helps

Answer: y = 6x-6

Step-by-step explanation:

Answer:

1

Step-by-step explanation:

Answer:

4th answer is correct

Step-by-step explanation:

First, let us make x the subject.

\(\sf \frac{x+4}{4} =\frac{y+7}{7}\)

Use cross multiplication.

\(\sf 7(x+4)=4(y+7)\)

Solve the brackets.

\(\sf 7x+28=4y+28\)

Subtract 28 from both sides.

\(\sf 7x=4y+28-28\\\\\sf7x=4y\)

Divide both sides by 7.

\(\sf x=\frac{4y}{7}\)

Now let us find the value of x/4.

To find that, replace x with (4y/7).

Let us find it now.

\(\sf \frac{x}{4} =\frac{\frac{4y}{7} }{4} \\\\\sf \frac{x}{4} =\frac{4y}{7}*\frac{1}{4} \\\\\sf \frac{x}{4} =\frac{4y}{28}\\\\\sf \frac{x}{4} =\frac{y}{7}\)

Answer:

Increases from points 0x,-6y to 2x,-3y.

Step-by-step explanation:

Answer:

B

Step-by-step explanation:

Formula

SA = 2*L*W + 2*L*H + 2*H*W

Givens

L = 14

W = 7

H = 7

Solution

SA = 2*14*7 + 2*14*7 + 2*7*7

SA = 196 + 196 + 98

SA = 490

The amount owed at the end of the 6 years duration is $10865

The given parameters about the compound interest are

Principal Amount, P = $5300

Interest Rate, R = 8%

Time, t = 6 years

To calculate the amount owed, we make use of the following formula

A = P + CI

Where

Compound interest, CI = P(1 + R)^t - P

So, the equation becomes

A = P + P(1 + R)^t - P

Evaluate the like terms

A = P(1 + R)^t

In this question, the formula is given as

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

Where

n = 12, i.e compounded monthly

Substitute the known values in the above equation

A = 5300 * (1 + 8%/12)^(6*12)

Express 8% as decimal

A = 5300 * (1 + 0.08/12)^(6*12)

Evaluate the sum

A = 5300 * (1.01)^(6*12)

Evaluate the exponent

A = 5300 * 2.05

Evaluate the product

A = 10865

Hence, the value of the amount after 6 years is $10865

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Answer:

x = 13

∠WZX = 57°

Step-by-step explanation:

Because it is a rectangle, ∠XYZ is 90°

∠XZY + ∠YXZ = 90

(5x - 8) + (x + 20) = 90

simplify:

6x + 12 = 90

subtract 12 from each side

6x = 78

divide both sides by 6

x = 13

∠WZX is complimentary to angle (x + 20)

∠WZX = 90 - (13 + 20) = 57°

Answer:

92°

Step-by-step explanation:

By exterior angle theorem:

\((2x - 2) \degree = x \degree + 45 \degree \\ \\ (2x - 2 - x) \degree = 45 \degree \\ \\ (x - 2) \degree = 45 \degree \\ \\ (x - 2) = 45 \\ \\ x = 45 + 2 \\ \\ x = 47 \\ \\ (2x - 2) \degree = (2 \times 47 - 2)\degree \\ \\ (2x - 2) \degree = (94 - 2)\degree \\ \\ (2x - 2) \degree = 92\degree \\ \\ measure \: of \: the \: exterior \: angle \\ = 92 \degree\)

Answer:

y=-sin(x)

Step-by-step explanation:

y=-sin(x)

answer: D.840 yards

Step-by-step explanation:

as to find volume of any 3 d shape we multiply l×b×h to find the volume

7×10×12=840

please mark as brainliest

Answer:

28

Step-by-step explanation:

\(7+7\times 3 = 7(1+3)= 7 \times 4 = 28\)

Answer:

28

Step-by-step explanation:

When we find the product of 2 or more numbers, we multiply them.

so

product of 7 and 3 = 7 x 3 = 21

7 + 21 = 28

Hope this helps. I attempted to make it as simple as possible.

- profparis

Answer:

not equivalent to meteorologists ratio

Step-by-step explanation:

meteorologists ratio is

rainy days : sunny days = 2 : 5

last months weather is

rainy days : sunny days

= 10 : 20 ( divide both parts by LCM of 10 )

= 1 : 2 ← not equivalent to 2 : 5

Answer:

3/4k^5+-1/2k^3

Step-by-step explanation:

You put the numbers in order from the largest exponent to the smallest.

The cost of the car will be less than or equal to $4,450.

What is a equation?

An equation is a mathematical statement that indicates the equality of two expressions. It contains one or more variables and usually includes mathematical operations such as addition, subtraction, multiplication, division, or exponentiation.

Let the cost of the car be "d" (in dollars). Then, the total expenses, including taxes and fees, can be expressed as:

Total expenses = Cost of the car + Taxes + Fees

We can represent the cost of the car as "d", and the taxes and fees as a fixed amount "t". Therefore, the equation to model Samantha's total expenses can be written as:

Total expenses = d + t

From the problem, we know that Samantha paid a total of $4,450 for the car, taxes, and fees. Therefore, we can write:

d + t = 4450

To find the cost of the car, we need to isolate the variable "d" on one side of the equation. We can do this by subtracting "t" from both sides of the equation:

d + t - t = 4450 - t

Simplifying the equation, we get:

d = 4450 - t

To determine the cost of the car, we need to know the value of "t", which represents the total taxes and fees. Unfortunately, the problem does not provide this information, so we cannot determine the exact cost of the car. However, we do know that the cost of the car will be less than or equal to $4,450, since the total expenses cannot be negative.

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According to the information, we can infer that the correct order for these number is -1.5, -0.75, -0.75, 1.25, 3.25.

To plot the numbers on a number line, we need to arrange them in increasing order. Here is the organized list of the numbers:

On the number line, we can mark -1.5 first and then move to the right to mark -0.75 twice (since it appears twice in the list), then 1.25, and finally 3.25 . On the number line, we can see that -1.5 is the smallest number and 3.25 is the largest number.

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A circle is a curve sketched out by a point moving in a plane. The length of wx is 18 cm.

A circle is a curve sketched out by a point moving in a plane so that its distance from a given point is constant; alternatively, it is the shape formed by all points in a plane that are at a set distance from a given point, the centre.

Given the length of the circle's diameter, z is 72 cm, therefore, the length of zx(Radius) is 36cm. Since the length of yz is 30 cm, the length of xy is 6 cm.

Also, the length of the circle's diameter, w is 48 cm, therefore, the length of wy(Radius) is 24 cm. Since the length of xy is 6 cm, the length of wx will be equal to,

Length of wx = wy-xy = 24cm - 6cm = 18 cm

Hence, the length of wx is 18 cm.

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As per the given measurement the centigrams of protein are in 3d fluid ounces of milk is 8504.86

The term measurement id known as the process of associating numbers with physical quantities and phenomena.

Here we know that one cup of skim milk contains 8 grams of protein.

Now, we have to find the amount of centigrams of protein are in 3d fluid ounces of milk.

As we all know that one ounce is equal to 2834.9553.

Then if we want the centigram value, then we have to multiply the number with 2834.9553, then we get the result as,

=> 3 x 2834.95

=> 8504.86

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Answer:

35

Step-by-step explanation:

answer

hx2

Step-by-step explanation:

From the data points given the linear equation in slope-intercept form is y = -1/2x + 4.

What is an equation?

A mathematical definition of an equation is a claim that two expressions are equal when they are joined by the equals sign ("=").

The first two data points are - (-3,5.5) and (-1,4.5)

The slope-intercept form of the equation is -

y = mx + b

m represents the slope of the linear equation.

To find the value of m use the formula -

(y2 - y1)/(x2 - x1)

Substitute the values into the equation -

(4.5 - 5.5)/[(-1) - (-3)]

Use the arithmetic operation of subtraction -

(-1)/(-1 + 3)

-1 / 2

So, the slope m is m = -1/2

Now, the equation becomes y = -1/2x + b

To find the value of b substitute the  values of x and y in the equation -

5.5 = -1/2(-3) + b

5.5 = 3/2 + b

5.5 = 1.5 + b

b = 5.5 - 1.5

b = 4

So, now the equation becomes - y = -1/2x + 4

The graph for the equation is plotted.

Therefore, the equation is y = -1/2x + 4.

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Answer:

Pls give me the answers as soon as possible and make sure that the answers are correct.

Answer:

Jewel is 7 years old

John is 1 year old

Dave is 17 years old

Step-by-step explanation:

From the question we are told that:

Jewel age is \(J=7 years\)

John age \(J'=(D-16)years\)

Dave's age a Year ago

 \(D-1=2(J-1+J'-1)\)

So that Dave.s age this Year could be

 \(D=2((J-1)+(J'-1))+1\)

Simplifying Equation for Dave's age we have

 \(D=2((7)-1+(D-16)-1)+1\)

 \(D=2(6+D-15)+1\)

 \(D=2(D-9)+1\)

 \(D=2D-18+1\)

 \(D=17 Years\)

Dave is 17 years old

Therefore

Johns age is

 \(J'=(D-16)\)

 \(J'=17-16\)

 \(J'=1year old\)

John is 1 year old