Perform the indicated operation 7 1/8×5 2/3

The exponential equation of the model is A(t) = 2583 * 0.88^t and the multiplier means that the number of new cases in a week is 88% of the previous week

The given parameters are:

New, A(t) = 2000

Rate, r = 12%

The function is represented as:

A(t) = A * (1 - r)^t

So, we have:

2000 = A * (1 - 12%)^t

This gives

2000 = A * (0.88)^t

2 weeks ago implies that;

t = 2

So, we have:

2000 = A * 0.88^2

Evaluate

2000 = A * 0.7744

Divide by 0.7744

A = 2583

Substitute A = 2583 in A(t) = A * 0.88^t

A(t) = 2583 * 0.88^t

Hence, the exponential equation of the model is A(t) = 2583 * 0.88^t

In this case, the multiplier is 88% or 0.88

This means that the number of new cases in a week is 88% of the previous week

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The paddling rate of Alvin is 9km/hr

Given time against the  river current is 10 hours , speed is 3km/hr

and time with the river current given is 5 hours and the speed is 3km/hr

We need to calculate the paddling rate of Alvin

Let us assume that

r =Alvin's average paddling rate in km/hour

y = speed of the current in km/hour

we know that

speed= distance/time

∴ distance=speed*time

Now,

To Campsite against the current

Speed=(r-y)

∴ Speed=(r-3) ---- (1)

Time=8 hours

Distance=(r-3)*10------ (2)

10r - 30

From Campsite with the current

Speed=(r+y)

∴Speed=(r+3)*5

Time=3 hours

Distance=(r+3)*5----(1)

Equate equation 1 and equation 2

5r +15

because is the same distance

5r + 15 = 10r - 30

5r = 45

r = 9

Hence ,The rate of the paddling rate is 9km/hr

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The location of the center of the circle is (h, k) = (4, 8) and the radius of the circle is equal to 2.5.

In this question we must determine the location of the center and the measure of the radius of a circle. According to Euclidean geometry, diameters are the longest possible chords of a circle. First, we determine the location of the center by definition of midpoint:

(h, k) = (1/2) · (4, 5.5) + (1/2) · (4, 10.5)

(h, k) = (4, 8)

And the radius is found by Pythagorean theorem:

[tex]d = \sqrt{(4 - 4)^{2}+(10.5-5.5)^{2}}[/tex]

d = 5

r = 0.5 · 5

r = 2.5

The location of the center of the circle is (h, k) = (4, 8) and the radius of the circle is equal to 2.5.

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Using the arrangements formula, the probability of the butterscotch, cinnamon, and then chocolate candies eaten in this particular order is:

[tex]\frac{1}{6}[/tex].

The number of possible arrangements of n elements is given by the factorial of n, that is:

[tex]A_n = n![/tex]

In this problem, there are 3 candies, hence the number of ways they can be eaten is:

[tex]A_3 = 3! = 6[/tex]

The desired order is only one, hence the probability is:

[tex]\frac{1}{6}[/tex].

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Answer:

the number 27 is a composite

Step-by-step explanation:

Yes, since 27 has more than two factors . 1, 3, 9, 27. In other words, 27 is a composite number because 27 has more than 2 factors

Answer:

The number 27 is composite.

The probability that a person chosen at random is younger than 65 is 0.967.

Probability calculates the odds that a random event would happen. The odds that the random event happens lie between 0 and 1.

The probability that a person chosen at random is younger than 65 = (total number of people younger than 65 / total number of respondents)

(350 + 412 + 318 + 200 + 107 + 51 ) / (350 + 412 + 318 + 200 + 107 + 51 + 49)

1438 / 1487 = 0.967

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Answer: The largest common factor of 28 and 32 is 4.

Step-by-step explanation:

The factors of 28 are 1, 2, 4, 7, 14, 28

The factors of 32 are 1, 2, 4, 8, 16, 32

Based on the triangle midsegment theorem, the midsegments and the sides they are parallel to are:

MP is parallel to XY

PZ is parallel to WX

MZ is parallel to WY

The segment that connects the midpoints of two sides of a triangle is referred to as the midsegment of the triangle. All triangles possess three midsegments. According to the triangle midsegment theorem, the third side of the triangle that is directly opposite the midsegment is twice the size of the midsegment and it is parallel to it.

In the diagram showing triangle WXY with midpoints at points M, Z, and P, the midsegments are:

MP which is parallel to XY, also, MP = 1/2(XY)

PZ which is parallel to WX, also, PZ = 1/2(WX)

MZ which is parallel to WY. also, MZ = 1/2(WY)

Thus, the midsegments and the sides they are parallel to are:

MP is parallel to XY

PZ is parallel to WX

MZ is parallel to WY

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The side lengths of rectangle is 3 cm and 1.75 cm  and  5.25 cm and  9 cm.

According to the statement

we have given that Rectangle A has side lengths of 6 cm  and 3.5 cm

And The side lengths of rectangle B are proportional to the side lengths of rectangle A.

And we have to Find that the What could be the side lengths of rectangle B?

A  3 cm and 1.75 cm

B  5 cm and  2.5 cm

C  7 cm and  7 cm

D  12 cm and  5 cm

E  5.25 cm  and  9 cm

Here we see that the side B are proportional to side length A of rectangle.

So,

Let say sides of rectangle B are  a  and  b  corresponding to sides  6 and 3.5 cm

=> a/6  = b/3.5

=> a/b = 6/3.5

=> a/b  = 12/7

A  3 cm and 1.75 cm    

3/1.75  = 12/7

Hence this is proportional

B  5 cm and  2.5 cm

5/2.5  = 2  ≠ 12/7

Not Proportional

C  7 cm and  7 cm

7/7 = 1 ≠ 12/7

Not Proportional

D  12 cm and  5 cm

12/5   ≠ 12/7

Not Proportional

E  5.25 cm  and  9 cm

9/5.25  = 36/21  = 12/7

Hence this is proportional

So, 3 cm and 1.75 cm   and   5.25 cm and  9 cm  could be the side lengths of rectangle B.

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Answer:

a.1

b.10

c.120

Step-by-step explanation: don't know that last one

The triangle is an isosceles triangle and the four triangles are similar

The coordinates are given as:

A (0, 0), B (5, 0), and C (2, 4).

Calculate the distance between the coordinates using:

[tex]d = \sqrt{(x_2 -x_1)^2 +(y_2 -y_1)^2[/tex]

So, we have:

[tex]AB = \sqrt{(0 -5)^2 +(0-0)^2} =5[/tex]

[tex]AC = \sqrt{(0 -2)^2 +(0-4)^2} =4.5[/tex]

[tex]BC = \sqrt{(5 -2)^2 +(0-4)^2} =5[/tex]

The above shows that two sides are congruent.

Hence, the triangle is an isosceles triangle

This is calculated using:

(x, y) = 0.5 * (x1 + x2, y1 + y2)

So, we have:

AB = 0.5 * (0 + 5, 0 + 0) = (2.5, 0)

AC = 0.5 * (0 + 2, 0 + 4) = (1, 2)

BC = 0.5 * (5 + 2, 0 + 4) = (3.5, 2)

From the attached graph, we can see that the triangles are similar

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Two ares are congruent if they have the same measure and lengths

The statement is given as:

Two ares are congruent if they have the same measure and ?

The conditions for congruent shapes in geometry are;

This means that the angle and the length must be equal

Hence, the term that completes the blank is length

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Answer:

x=20

Step-by-step explanation:

x-15=5

x=5+15

x=20

Answer:

d.

Step-by-step explanation:

Given a length [tex]l[/tex] and a width [tex]w[/tex], we can express the perimeter of a rectangle as [tex]2(l+w)[/tex].

Therefore the perimeter [tex]P[/tex] can be expressed as

[tex]2\times[(x-8)+(x-9)]\\=2\times(2x-17)\\=4x-34[/tex]

Answer:

x=30,y=165,z=5

Step-by-step explanation:

check it bro

Answer:

[tex]\frac{\sqrt{41}}{4}[/tex]

Step-by-step explanation:

sec(theta) is defined as: [tex]sec(\theta)=\frac{1}{cos(\theta)} = \frac{hypotenuse}{adjacent}[/tex]

In the diagram you provided the hypotenuse of the triangle is sqrt(41) and the opposite side is 5, using these two sides, we can solve for the adjacent side by using the Pythagorean Theorem: [tex]a^2+b^2=c^2[/tex]

So this gives us the equation where a=adjacent side:

[tex]a^2+5^2=\sqrt{41}^2[/tex]

[tex]a^2+25=41[/tex]

Subtract 25 from both sides

[tex]a^2=16[/tex]

Take the square root of both sides

[tex]a=4[/tex]

So now plug this into the definition of sec(theta) and you get: [tex]\frac{\sqrt{41}}{4}[/tex]. This is in most simplified form since 41, has no factors besides 41 and 1.

Answer:

Step-by-step explanation:

The slope of the median of the triangle whose vertices are P(-6,1),Q(-2,5) R(8,1) and passes through R is -1/6.

Given that vertices of triangle is P(-6,1),Q(-2,5),R(8,1) and there is a median which passes through R.

Median of a triangle is a line segment which originates from a vertex of triangle and divides the opposite side in two equal parts. let median touches the line at L point.

When line passes through R then it must be a perpendicular on PQ. The coordinates of L is {(-2-6)/2,(5+1)/2}=(-4,3)

Now because median passes through R,it will be LR and we know that the formula of calculating slope of line from two points is [tex](y_{2} -y_{1} )/(x_{2} -x_{1} )[/tex] where [tex](x_{1} ,y_{2} ),(x_{2} ,y_{2} )[/tex] are the points of the end points of line.

Slope=(1-3)/(8+4)

=-2/12

=-1/6

Hence the slope of the median of the triangle whose vertices are P(-6,1),Q(-2,5) R(8,1) and passes through R is -1/6.

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The inequalty that represents the statement must be y < - 6 · (x + 2)² + 2. (Right choice: None)

The standard form of the equation of the parabola is defined by the following expression:

y - k = C · (x - h)²     (1)

Where:

Now we proceed to find the vertex constant: (h, k) = (- 2, 2) and (x, y) = (- 4, 14)

14 - 2 = C · [- 4 - (- 2)]²

12 = C · (-2)

C = - 6

The equation of the parabola in vertex form is

y - 2 = - 6 · (x + 2)²

y = - 6 · (x + 2)² + 2

Then, the inequalty that represents the statement must be y < - 6 · (x + 2)² + 2. (Right choice: None)

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Answer:

y < 3(x + 2)2 + 2

Step-by-step explanation:

just do it

Reflection and dilation is the transformation which will occur to map triangle ABC triangle to A^ * B^ n C^ prime.

This refers to a plane figure which has features such as three angles and three sides.

Reflection and dilation involves flipping and enlargement/reduction respectively which gives rise to the sides being changed.

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Answer:

c. a reflection and a dilation

Step-by-step explanation:

Using the least common factor, they need to wait 14 days until they next get to work together.

To find the time that passes between the events happening at the same time, we need to find the least common multiple of the periods.

In this problem, the periods are of 2 days and 7 days, which already are prime numbers, hence:

lcm(2,7) = 2 x 7 = 14.

They need to wait 14 days until they next get to work together.

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Using the hypergeometric distribution, the probabilities are given as follows:

a) 0.2 = 20%.

b) 0.5539 = 55.39%.

The formula is:

[tex]P(X = x) = h(x,N,n,k) = \frac{C_{k,x}C_{N-k,n-x}}{C_{N,n}}[/tex]

[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]

The parameters are:

Researching this problem on the internet, it is found that the council has 15 members, of which 7 are Democrats and 8 are Republicans.

Item a:

The parameters are:

N = 15, n = 2, k = 7.

The probability is P(X = 2), hence:

[tex]P(X = x) = h(x,N,n,k) = \frac{C_{k,x}C_{N-k,n-x}}{C_{N,n}}[/tex]

[tex]P(X = 2) = h(2,15,2,7) = \frac{C_{7,2}C_{8,0}}{C_{15,2}} = 0.2[/tex]

Item b:

At most one Democrat, with n = 3, hence:

[tex]P(X \leq 1) = P(X = 0) + P(X = 1)[/tex]

In which:

[tex]P(X = 0) = h(0,15,3,7) = \frac{C_{3,0}C_{8,3}}{C_{15,3}} = 0.1231[/tex]

[tex]P(X = 1) = h(1,15,3,7) = \frac{C_{3,1}C_{8,2}}{C_{15,3}} = 0.4308[/tex]

Then:

[tex]P(X \leq 1) = P(X = 0) + P(X = 1) = 0.1231 + 0.4308 = 0.5539[/tex]

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Using proportions, the numbers that the arrows are pointing to are:

a) 62.

b) 8.8.

c) 2.8.

A proportion is a fraction of a total amount, and the measures are related using a rule of three.

In item a, the arrow is 2/10 of the way from 60 to 70, hence the number is:

60 + 0.2(70 - 60) = 60 + 2 = 62.

In item b, the arrow is 8/10 of the way from 8 to 9, hence the number is:

8 + 0.8(9 - 8) = 8.8.

In item c, the arrow is 3/10 of the way from 2.5 to 3.5, hence the number is:

2.5 + 0.3(3.5 - 2.5) = 2.8.

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Based on the given situation, Max final number if his starting number is 7 is -4.5

n + 8

2(n + 8)

So,

2(n + 8) = 7

2n + 16 = 7

2b = 7 - 16

2n = -9

n = -9/2

n = -4.5

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Based on the graph which depicts the United States domestic market for  corn at different prices, we can logically deduce the following information:

Assuming France is the only other corn-producing nations at a domestic price of $4, we can reasonably infer that the United States will export corn while France will import it.

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Answer: i+96

Step-by-step explanation:

Note that [tex]i^{4k}[/tex], where k is an integer, is equal to 1.

This means that [tex]i^{4!}=i^{5!}=i^{6}=\cdots=i^{99!}+i^{100!}=1[/tex]

So, we can rewrite the sum as [tex]i^{1}+i^{1}+i^{2}+i^3+97(1)=i+i-1-i+97=i+96[/tex]

[tex]n![/tex] is divisible by 4 for all [tex]n\ge4[/tex]. This means, for instance,

[tex]i^{4!} = \left(i^4\right)^{3!} = 1^{3!} = 1[/tex]

[tex]i^{5!} = \left(i^4\right)^{5\times3!} = 1^{5\times3!} = 1[/tex]

etc, so that [tex]i^{n!} = 1[/tex] for all [tex]n\ge4[/tex].

Meanwhile,

[tex]i^{0!} = i^1 = i[/tex]

[tex]i^{1!} = i^1 = i[/tex]

[tex]i^{2!} = i^2 = -1[/tex]

[tex]i^{3!} = i^6 = (-1)^3 = -1[/tex]

Then the sum we want is

[tex]i^{0!} + i^{1!} + i^{2!} + i^{3!} + 97\times1 = i + i - 1 - 1 + 97 = \boxed{95+2i}[/tex]

The expanded form of the given exponential equation is 6718464

Exponential equations are inverse of logarithmic equations. The standard exponential equation is expressed as. y = ab^x

where

a is the base

x is the exponent

Given the expression below;

a = 4(6)^8​

Expand to have:

a = 4 * 6 * 6 * 6 * 6 * 6 * 6 * 6 * 6

a = 4 * 1679616
a = 6718464

Hence the expanded form of the given exponential equation is 6718464

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[tex]\begin{gathered} 9 - 4\sqrt{5} \\ \\ = 4 + 5 - 4\sqrt{5} \\ \\ = (- 2)^2 + (\sqrt{5})^2 + (2 \times - 2 \times \sqrt{5}) \\ \\ = (- 2 + \sqrt{5})^2 \\ \\ = (\sqrt{5} - 2)^2 \\ \\ \\ \therefore \sqrt{9 - 4\sqrt{5}} = \sqrt{5} - 2 \end{gathered}[/tex]

Hope this may be helpful.

Answer:

x=6

Step-by-step explanation:

This is a vertical line going through (6,0).  If you take this point and the point given and calculate the slope you find the change in y over the change in x.  

0-(-3)/6-6  The slope is undefined because the denominator of the slope would be zero.

Answer:

Well a sovial reason is that no one would no what order yo do it in, which would cause arguments

Answer:

without the order of operations, maths literally doesn't work.

Step-by-step explanation:

like whilst some equations don't rely on a particular order for solving, if you for example, don't solve brackets first, then try to multiply them by something else basically the equation breaks and you get the wrong answer. So... kids remember your BODMAS :)