Make y the subject of the relation;
m over y = tan 46⁰​

Answer:

15x^2 + 25x + 10

Step-by-step explanation:

The area of the rectangle is equal to multiplication of the base and side lengths

height = 5x + 5

side = 3x + 2

(5x + 5) × (3x + 2) = 15x^2 + 10x + 15x + 10

Answer: 15x^2 +25x + 10

Step-by-step explanation:

The Area of the Rectangle is the Width multiplied by the heigh.

(5 X + 5)(3x +2)

15x^2 + 10 x + 15 x + 10

15x^2 + 25x + 10

Answer:

23.5

Step-by-step explanation:

So this is a parallelogram so the area formlula is b*h=47? That's a no go. It is saying that if the base is 1/4th and the height is increasing by 2 so basically 1/4b*2h=1/2bh bh so it will be represented as 47 so 1/2*47=23.5

Answer:

263 cents

Step-by-step explanation:

Answer:

263¢

Step-by-step explanation:

Answer:

In what time frame. It asks how often she does both but does that mean in a week or another span of time?

Step-by-step explanation:

Answer:

there is no shape below

A) Approx. 1067 is the required sample size to ensure 95% confidence that the sample proportion will not differ from the true proportion by more than 3%.

B) When the previous estimate is 65%, approx. 971 is the sample size needed to achieve 95% confidence that the sample proportion will not differ by more than 3% from the true proportion.

To determine the sample size needed for estimating the proportion of drivers exceeding the speed limit, we can use the formula for sample size calculation for proportions:

n = (Z² * p * (1 - p)) / E²

where:

n = the sample size.

Z = the Z-value associated with the confidence level of 95%.

p = the estimated proportion or previous estimate.

E = the maximum allowable error, which is 3% or 0.03.

We calculate as follows:

A. No previous estimate for p is available:

Here, we will assume p = 0.5 (maximum variance) since we don't have any prior information about the proportion. So, adding the values into the formula:

n = (Z² * p * (1 - p)) / E²

n = ((1.96)² * 0.5 * (1 - 0.5)) / 0.03²

n= (3.842 * 0.5 * (0.5))/0.03²

n = (1.9208*0.5)/0.0009

n ≈ 1067.11

Thus, to be 95% confident that the sample proportion will not differ from the true proportion by more than 3%, a sample size of approximately 1067 is required.

B. Supposing previous studies found that the sample percentage of drivers who exceeded the speed limit is 65%:

Here, we have a previous estimate of p = 0.65:

Putting the values into the formula:

n = (Z²* p * (1 - p)) / E²

n = ((1.96)² * 0.65 * (1 - 0.65)) / 0.03²

n= (3.842 * 0.65 *(0.35))/0.0009

n ≈ 971

Hence, with the previous estimate of 65%, a sample size of approximately 971 is necessary to be 95% confident that the sample proportion will not differ from the true proportion by more than 3%.

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Answer:

Vertex angle = 124°

Step-by-step explanation:

m<BAC = m<BCA (base angles of isosceles ∆ are congruent)

7x + 1 = 5x + 9

Collect like terms

7x - 5x = -1 + 9

2x = 8

divide both sides by 2

x = 4

Vertex angle = 180 - ((7x + 1) + (5x + 9)) (sum of triangle)

Plug in the value of x

Vertex angle = 180 - ((7*4 + 1) + (5*4 + 9))

Vertex angle = 180 - (29 + 29)

Vertex angle = 124°

The equation of a line in the slope intercept form is expressed as

y = mx + c

Where

m represents slope

c represents y intercept

The formula for determining slope is

m = (y2 - y1)/(x2 - x1)

From the information given,

x1 = 2, y1 = 5

x2 = 1, y2 = 8

m = ((8 - 5)/(1 - 2) = 3/- 1

m = - 3

we would find the y intercept, c by substituting x = 2, y = 5 and m = - 3 into the slope intercept equation. It becomes

5 = - 3 * 2 + c

5 = - 6 + c

c = 5 + 6 = 11

We would substitute m = - 3 and c = 11 into the slope intercept equation. Thus, the equation of the line is

y = - 3x + 11

Answer:

A

Step-by-step explanation:

A looks good to me why?

Well:  31 x -10= -310 - true

Could I get brinliest pls Tysm if u do!

Hope this helps :D

Answer:

8.5 quarts

Step by step explanations:

divide the volume value by 2

Answer:

Step-by-step explanation:

f(n)= -3n + 2

to find :f(12)

substitute 12 in place of n

f(12)= -3*12 + 2

f(12)=-36 + 2

f(12)= -34

The value of the  f(12) is equal to -46 where the expression is

f(n) = -3n + 2.

Any mathematical statement which consist of numbers , variables and arithmetic operations is known as expression. An expression gives some numerical value when we put the value of variables in it.

Here, f(n)= -3n + 2 is the given expression.

So, we can find the value of f(12) by putting n=12 in f(n).

Put n=12 in f(n), we get

          f(12)= (-3)×12 + 2

                 = -48 + 2

                 = -46

Hence, the value of f(12) is -46.

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Step-by-step explanation:

Use the Factor Theorem,

" if x-a is a factor of f(x), then f(a) =0,

So here, since x-3 is a factor then f(3)=0,

So first step, plug in 3 for x for the serperate equations.

\( {3}^{2} + ( p + q)3 - q = 0\)

\(2(3) {}^{2} + (p - 1)3 + (p + 2q) = 0\)

Simplify both equations,

\(9 + 3p + 2q = 0\)

\(15 + 4 p + 2q = 0\)

Isolate the constants,

\(3p + 2q = - 9\)

\(4p + 2q = - 15\)

We have a system of equations so let eliminate a variable, by subtracting the two equations.

\( - p = 6\)

\(p = - 6\)

Plug p back in for any one of the equations to find q.

\(3( - 6) + 2q = - 9\)

\( - 18 + 2q = - 9\)

\(2q = 4.5\)

So p is -6

q is 4.5

The total surface area of the solid object is 2660.925 square cm the answer is 2660.925 square cm.

In geometry, it is defined as the three-dimensional shape having two circular shapes at a distance called the height of the cylinder.

We know the volume of the cylinder is given by:

\(\rm V = \pi r^2 h\)

The surface area of the

= surface area of half sphere + surface area of the cylinder - surface area

  of one circular base

The radius r = (64-50)/2 = 7 cm

= (1/2)[4π(7)²] + 2π(7)(50) + 2π(7)² - π(7)²

= (1/2)[615.75] + 2506.99 - 153.94

= 307.875 + 2506.99 - 153.94

= 2660.925 square cm

Thus, the total surface area of the solid object is 2660.925 square cm the answer is 2660.925 square cm.

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Answer:

Salem = 50 + 5x

Dated = 90 + 5x

Step-by-step explanation:

The 50 baseball cards Salem starts with and the 90 Dated starts with is fixed and the 5 they plan to buy per month is variable. As the months go by, the number of baseball cards increases by 5.

After 12 months, the number of baseball cards

Salem would have = 50 + 5(5) = 75

Dated would have = 90 + 5(5) = 115

Let x represent the number of months, so we would have the following equations  :

50 + 5x

90 + 5x

Answer:

\(842\ \text{ft}\)

\(y(t)=906-16t^2\)

Step-by-step explanation:

Let \(y\) be the height the object from the ground.

\(s\) be the initial height of the object = 906 ft

\(u\) = Initial velocity = 0

\(g\) = Acceleration due to gravity = \(32\ \text{ft/s}^2\)

\(t\) = Time

The expression would be

\(y(t)=s-ut-\dfrac{1}{2}gt^2\\\Rightarrow y(t)=906-16t^2\)

The required expression is \(y(t)=906-16t^2\)

At \(t=2\ \text{s}\)

\(y(2)=906-16\times 2^2\\\Rightarrow y(2)=842\ \text{ft}\)

The height of the object after 2 seconds of falling is \(842\ \text{ft}\).

Answer:

I think it is B but i'm not 100% sure.

Step-by-step explanation:

The journey which is supposed to start 16:24pm but started 7 minutes later and ended 17 : 17pm took 46 minutes.

Original take off time of the bus = 16:24pm.

The bus leaves 7 minutes later

New take off time of the bus = 16:24pm + 7 minutes

= 16:31 pm

Time of arrival of the bus = 17 : 17pm.

Time taken on the journey = Time of arrival of the bus - New take off time of the bus

= 17 : 17pm - 16:31 pm

= 46 minutes

Ultimately, the journey took 46 minutes from the time of departure to the time of arrival.

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Answer:

wouldn't this be 4,2?

Step-by-step explanation:

i remember doing this in school last year and dilation means you would multiple the coordinates by what ever the dilation factor was, in this case its 2.

Answer:

7 = The y-intercept of the exponential function

1 = The y-intercept of the linear function

2 = The number of points of intersection

5 = The y-value of the solution in Quadrant I

Tell me if i'm wrong

The line y = -x, passing through the origin in the xy-plane, forms a 45-degree angle with the positive x-axis.

The slope-intercept form of a linear equation is y = mx + b, where m represents the slope of the line. In this case, the equation y = -x has a slope of -1. The slope indicates the ratio of the vertical change (rise) to the horizontal change (run) between two points on the line.

To determine the angle between the line and the positive x-axis, we need to find the angle that the line's slope makes with the x-axis. Since the slope is -1, the line rises 1 unit for every 1 unit it runs. This means the line forms a 45-degree angle with the x-axis.

The angle can also be determined using trigonometry. The slope of the line (-1) is equal to the tangent of the angle formed with the x-axis. Therefore, we can take the inverse tangent (arctan) of -1 to find the angle. The arctan(-1) is -45 degrees or -π/4 radians. However, since the line is in the positive x-axis direction, the angle is conventionally expressed as 45 degrees or π/4 radians.

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It will take about 387.3 months (or about 32.3 years) to triple the balance of the account.

What is Compound Interest ?

Compound interest refers to the process of earning interest on both the initial principal amount as well as any accumulated interest from previous periods. In other words, it is the interest that is earned on the interest that has been accumulated over time.

We can use the formula for compound interest to solve this problem.

Where:

A = the final amount

P = the initial amount

r = the annual interest rate (as a decimal)

n = the number of times the interest is compounded per year

t = the time (in years)

In this problem, we have:

P = $250

r = 0.06% = 0.0006 (as a decimal)

n = 12 (since the interest is compounded monthly)

A = 3P = $750

Substituting these values into the formula, we get:

750 = 250\((1 + 0.0006/12) ^{12t}\)

Dividing both sides by 250, we get:

3 =\((1 + 0.0006/12) ^{12t}\)

Taking the natural logarithm of both sides, we get:

㏒(3) = 12t ㏒(1 + 0.0006÷12)

Solving for t, we get:

t = ㏒(3)/(12 ㏒(1 + 0.0006÷12))

Plugging this into a calculator, we get:

t ≈ 387.3 months

Therefore, it will take about 387.3 months (or about 32.3 years) to triple the balance of the account.

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Answer: Let's assume the exchange rate between ZAR and EUR is given by E1, and the exchange rate between ZAR and CAD is given by E2.

First, let's calculate the cost of the CD in ZAR:

5 EUR * E1 = 5 * E1 ZAR

Next, let's calculate how much money Teboho will have left after purchasing the CD:

250 ZAR - 5 * E1 ZAR = 245 ZAR - 5 * E1 ZAR

Now, let's calculate the cost of the CD in CAD:

7 CAD * E2 = 7 * E2 ZAR

We need to determine the value of E1 and E2 in order to compare the prices. However, without knowing the current exchange rates, we cannot determine the best option for Teboho. If the exchange rate between ZAR and EUR is favorable and the cost of the CD in ZAR is lower than the cost of the CD in CAD, Teboho should order the CD from Germany. On the other hand, if the exchange rate between ZAR and CAD is favorable and the cost of the CD in CAD is lower than the cost of the CD in EUR, Teboho should order the CD from Canada.

Step-by-step explanation:

The explicit formula for the given sequence is\($-2 n+10$\).

Given sequence is-

\($$8,6,4,2,0 \text {, }$$\)

In the given sequence there is a common difference of $-2$ in two successive terms so the given sequence is an arithmetic sequence.

Here

first term\($\left(a_1\right)=8$\)

common difference \($(d)=-2$\)

So the explicit formula for the nth term of the given sequence-

\(& a_n=a_1+(n-1) d \\\)

\(& a_n=8+(n-1)(-2) \\\)

\(& a_n=8-2 n+2 \\\)

\(& a_n=-2 n+10\)

So the explicit formula for the given sequence is \($-2 n+10$\)

Now

\(& a_{14}=-2(14)+10 \\\)

\(& a_{14}=-28+10 \\\)

\(& a_{14}=-18\)

So \($a_{14}=-18$\) is the required answer.

Also, explicit formula for the given sequence is\($-2 n+10$\).

The complete question is,

Write an explicit formula for the sequence 8,6,4,2,0, ...Then find \($a_{14}$\).

\(& -a_n=-2 n+10 ;-16 \\\)

\(& -a_n=-2 n+8 ;-18 \\\)

\(& -a_n=-2 n+8 ;-20 \\\)

\(& -a_n=-2 n+10 ;-18\)

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Given:-

The line passes through (-7,9).

To find:-

Equation for a line that parallel to y-axis and passes through the point (-7,9).

The images of line which is parallel to y-axis is,

So if the line is parallel towards the y-axis then, the value of x-axis is equal.

That is,

And the value of k here is the x-axis value of the point the line passes through.

So,

So the equation of the line which is parallel to y-axis and passes through the point (-7,9) is,

So the required equation is x+7=0.

Answer:

  12.68

Step-by-step explanation:

The relevant trig relation is ...

  Sin = Opposite/Hypotenuse

In this instance, we have ...

  sin(25°) = x/30

  x = 30·sin(25°)

  x ≈ 12.68

Answer: The sales tax paid is $3.22.

Explanation: 38.22 - 35 = 3.22.

Answer:

1/4 is used for warehouse workers.

Step-by-step explanation:

If 1/4 is used for management and 1/2 are used for sales, together, that's only a total of 3/4 leaving 1/4 left for warehouse workers.

Hope this helps.

Answer:

15 rooms (1/4)

Step-by-step explanation:

No of rooms for the management: 60 × 1/4 = 15

No of rooms for the sales: 60 × 1/2 = 30

No of rooms for warehouse workers: Total rooms - (No of rooms for the management + No of rooms for the sales)

= 60 - (15 + 30)

= 60 - 45

= 15

The number of rooms for the warehouse workers is 15 (which is 1/4 of the total number of rooms).

The formula speed = distance ÷ time can be rearranged, just like any other equation. The formula can be rearranged in three ways: speed = distance ÷ time , distance = speed × time.

Speed tells us how slow or fast an object moves.  Distance refers to extent of space between two events. Time refers to an interval separating two events.

ASSUME a ferry travels 1/7th of the distance between two ports in 3/5 hours , then it will be able to cover 5/6th part of the distance between two ports  in 3.5 hours.

Distance that the ferry would be able to trave in 1 hour can be found out by :

unit rate=distance / time

=1/7÷3/5

Reciprocal:

=1/7×5/3

=5/21th of distance per hour

The distance that the ferry would be able to travel in 3.5 hours:

= (5/21 ) ×3.5

=(5/21)×(7/2)

Further solving:

=(5/3)×(1/2)

5/6th of the distance between two ports.

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Complete question could be a ferry travels 1/7th of the distance between two ports in 3/5 hours , then it will be able to cover 5/6th part of the distance between two ports  in 3.5 hours.

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