Here is a 5 by 8 grid
Create a design so that the ratio of unshaded squares to shaded squares is 3 : 2

One of the conditions for forming a triangle is:

The sum of the length of any two sides of a triangle is greater than the length of the third side.

i.e. if we have this triangle:

The condition means:

Let us now apply this condition to the question.

I. If the third side is the largest side:

We have been given two sides with lengths 8 and 17.

Let us make a = 8 and b = 17 and c is the third side

Using the condition we have:

This implies that the length of the third side must be less than 25.

II. If the third side is the smallest side:

Again let us make a = 8 and c = 17 and b is the third side

Using the condition, we have:

This implies that the length of the third side must be greater than 9.

Therefore the answer is Option D

Answer:

Point C will be at (3,1), Point B will be at (7,1) and Point A will be at (7,5)

Step-by-step explanation:

9514 1404 393

Answer:

  a) $608.05

  c) $72,966

  e) $11,766

  g) $19,935

Step-by-step explanation:

The formula for the monthly payment amount on a loan of P at rate r for t years is ...

  A = P(r/12)/(1 -(1 +r/12)^(-12t))

For the standard repayment plan, t = 10. You have P = $61,200 and r = 0.036, so the formula becomes ...

  A = $61,200(0.036/12)/(1 -(1 +0.036/12)^(-12·10))

  = $61,200(0.003)/(1 -1.003^-120)

  = $608.05

a) The monthly payment under the standard repayment plan is $608.05.

__

c) The total of 12 payments per year over 10 years is ...

  $608.05×10×12 = $72,966.00

__

e) The interest paid is the difference between payments and the amount borrowed:

  interest = $72,966 -61,200 = $11,766

__

g) Payments under the extended repayment plan last for 25 years (300 months). They will be $309.67 (found using a financial calculator). The total of those payments will be $309.67×300 = $92,901. Your savings under the standard plan are ...

  $92,901 -72,966 = $19,935

_____

Additional comment

Many graphing calculators have apps for figuring loan payments or other parameters. Spreadsheets have these functions, too.

Here, we have rounded the loan payment value to the nearest cent. This means the payment differs slightly from the computed value. In the real world, the final loan payment will be different from the rest, so as to take care of this discrepancy. In addition to the unpaid principal, there will be an interest charge that depends on the precise day on which the final payment is made.

We're never quite sure how accurate the answer is expected to be, so we've done the calculations using the loan payment value we came up with.

Segment AC = AB + BC

AB = x + 2 + 7x -3

Combine like terms:

AB = 8x - 1

QR = PR - PQ

QR = 13y + 25 - (8y + 5)

13y -8y = 5y

25-5 = 20

QR = 5y + 20

Answer:

y=-4/3x+13

Step-by-step explanation:

formula:y=mx+b

you need to add 9 on both sides of the equation

so it's look like this:y-9=-4/3x+5

                                  +9          +9

so combine the like terms

y=-4/3x+13

Answer:

4.28%

Step-by-step explanation:

We Know

Last year you earned $72,400

This year you earned $75,500

What was the rate of change in your earnings since last year?

We Take

(75,500 ÷ 72,400) x 100 ≈ 104.28%

Then We Take

104.28 - 100 = 4.28%

So, the earning increased by about 4.28%.

The insurance company would pay a total of $101,000 for the medical expenses resulting from the accident.

In this scenario, Sally's car insurance policy has coverage limits of 100/300/50. These numbers represent the maximum amount the insurance company will pay for different types of damages in an accident. Let's break down what these numbers mean in the context of the collision.

The first number, 100, represents the maximum amount (in thousands of dollars) that Sally's insurance company will pay for bodily injury per person. Since Sally sustained $150,000 in injuries and her passenger sustained $1,000 in injuries, the insurance company will cover Sally's medical expenses up to the policy limit, which is $100,000.

The second number, 300, represents the maximum amount (in thousands of dollars) the insurance company will pay for bodily injury per accident. In this case, both Sally and her passenger were injured, so the insurance company will cover their combined medical expenses up to the policy limit, which is $300,000.

The third number, 50, represents the maximum amount (in thousands of dollars) the insurance company will pay for property damage per accident. However, since the question only mentions injuries and not property damage, we can disregard this number for now.

Therefore, the total medical expenses the insurance company would pay for this accident would be $100,000 for Sally's injuries and $1,000 for her passenger's injuries, totaling $101,000.

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Answer:

a)  963g

b) 17

Step-by-step explanation:

i) Now we must first find the common difference of the AP

d = 7.8 -6 = 1.8

Now the sum of the AP gives the total amount of chemical used for 30 experiments

Sn = n/2 [2a + (n-1)d]

n= 30, a = 6, d= 1.8

Sn = 30/2[2(6) + (30-1) (1.8)]

Sn = 15[12 + 52.2]

Sn = 963g

ii)For the G.P the common ration is (r)= 7.8/6 = 1.3

Since r>1, sum of GP = a (r^n -1)/r-1

If sum =  1800g

1800= 6(1.3^n -1)/1.3 - 1

1800 = 6(1.3^n -1)/0.3

1800 * 0.3  = 6(1.3^n -1)

540 = 6(1.3^n -1)

540/6 = (1.3^n -1)

90 = 1.3^n -1

90 + 1 = 1.3^n

1.3^n = 91

log 1.3^n = log 91

nlog1.3 = log 91

n = log91/log 1.3

n = 1.959/0.114

n = 17

Answer:

a)  963g

b) 17

Step-by-step explanation:

i) Now we must first find the common difference of the AP

d = 7.8 -6 = 1.8

Now the sum of the AP gives the total amount of chemical used for 30 experiments

Sn = n/2 [2a + (n-1)d]

n= 30, a = 6, d= 1.8

Sn = 30/2[2(6) + (30-1) (1.8)]

Sn = 15[12 + 52.2]

Sn = 963g

ii)For the G.P the common ration is (r)= 7.8/6 = 1.3

Since r>1, sum of GP = a (r^n -1)/r-1

If sum =  1800g

1800= 6(1.3^n -1)/1.3 - 1

1800 = 6(1.3^n -1)/0.3

1800 * 0.3  = 6(1.3^n -1)

540 = 6(1.3^n -1)

540/6 = (1.3^n -1)

90 = 1.3^n -1

90 + 1 = 1.3^n

1.3^n = 91

log 1.3^n = log 91

nlog1.3 = log 91

n = log91/log 1.3

n = 1.959/0.114

n = 17

Answer:

2(-g+2)

Step-by-step explanation

Answer: −2g+4

Step-by-step explanation:

I attached image of explanation! Hope this helps!

The length of AD is 1 unit.

A triangle is a three-sided polygon that consists of three edges and three vertices.

Let us solve the question

In Δ ABC

∠B is a right angle

BD is perpendicular to the hypotenuse AC

(AB)² = AD × AC ⇒ rule

AB = 3 units

AC = 9 units

Let AD = x

Substitute them in the rule above

(3)² = x × 9

9 = 9x

Divide both sides by 9

x=1

Hence, the length of AD is 1 unit.

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Question

Given right triangle ABC with altitude BD drawn to hypotenuse AC. If AB = 3 and AC = 9, what is the length of AD? (Note: the figure is not drawn to scale.)

The inequality value that would be able to show/x/ ≤ 5 is option A

In mathematics, inequality refers to a mathematical statement that expresses a relationship between two quantities, indicating that one quantity is greater than, less than, or not equal to the other.

The symbol that we have  is telling us that the value of the x would be less than  or it would be seen to be equal to five.

We can see that /x/ ≤ 5 would exclude the negative values and this can be seen in the option that is marked option A

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Answer:

Step-by-step explanation:

The volume of this pyramid in cubic inches is 16.

Given that,

The base and height is 8 and 6.

Based on the above information, the calculation is as follows:

The volume is

= 16

Answer:

Step-by-step explanation:

A school bag contains 12 pens of which 5 are red and the other are black. 4 pens are selected from the bag.

(a) How many different samples of size 4 pens are possible?

12C4=12!/(4!*8!)=495

(b) How many samples have 3 red pens and 1 black pen?

5C3*7C1

5C3=5!/(3!*2!)=10

7C1=7!/(1!*6!)=7

=>5C3*7C1=10*7=70

(c) How many samples of size 4 contain at least two red pens?

(5C2*7C2)+(5C3*7C1)+(5C4*7C0)

5C2=5!/(2!*3!)=10

7C2=7!/(2!*5!)=21

5C3=5!/(3!*2!)=10

7C1=7!/(1!*6!)=7

5C4=5!/(4!*1!)=5

7C0=7!/(0!*7!)=1

=>(5C2*7C2)+(5C3*7C1)+(5C4*7C0)=285

(d) How many samples of size 4 contain at most one black pen?

(7C1*5C3)+(7C0*5C4)

7C1=7!/(1!*6!)=7

7C0=7!/(0!*7!)=1

5C3=5!/(3!*2!)=10

5C4=5!/(4!*1!)=5

=>(7C1*5C3)+(7C0*5C4)=(7*10)+(1*5)=75

Step-by-step explanation:

True...it was Answer but not in always

Answer: \(73^{\circ}\)

Step-by-step explanation:

Angles in a triangle add to 180 degrees.

Step-by-step explanation:

I am not sure that you typed it all correctly.

but based on what is written here

f(x) = x²

g(x) = sqrt(x) + 2

so, g(f(2)) + f(1) = g(2²) + 1² = g(4) + 1 = sqrt(4) + 2 + 1 =

= 2 + 2 + 1 = 5

The angle θ that is coterminal with angle 14π/3, is 20π/3

Coterminal angles are the angles that have the same initial side and share the terminal sides. These angles occupy the standard position, though their values are different. They are on the same sides, in the same quadrant and their vertices are identical.

Given that, we need to find a coterminal angle of 14π/3,

The formula to find the coterminal angles is, θ ± 2πn where, n is an integer and it denotes the number of rotations around the coordinate plane.

For finding one coterminal angle: n = 1 (anticlockwise)

Then the corresponding coterminal angle is,

= 14π/3 + 2πn

= 14π/3 + 2π(1)

= 14π/3 + 2π

= 20π/3

Hence, the angle θ that is coterminal with angle 14π/3, is 20π/3

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Answer:

I dont really know

Step-by-step explanation:

Answer:

  128 g

Step-by-step explanation:

Ronald's share of the strawberries can be found from the proportion ...

  ronald's/total = 8/(2+8)

  ronald's = (160 g)(8/10) = 128 g

Ronald got 128 g of strawberries.

_____

William got 32 g.

Step-by-step explanation:

total ratio=10

William's ratio=2

Roland's ratio=8

Roland's share=8/10×160g

=4/5×160g

Roland's share =128g.

For the time period of  the projectile at least 192 feet above the ground is between 2 second and 6 second

Since s=128t-16t2, we want to know the 2 times where 128t-16t2=192, as those two values will be the begin and end times of the interval in question. We can rewrite that equation in standard quadratic equation form:

16t2-128t+192=0 or, simplified, 8t2-64t+96=0

or t2-8t+12=0

since it is now in quadratic form, we can solve using the quadratic formula:

t = 2 and 6

So the time period from approximately 2 second and 6 second has the projectile above 192 feet.

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Answer:

The probability that on a particular week, the hospital will receive on high BP pregnant woman is 0.0068

Step-by-step explanation:

We use the Exponential distribution,

Since we are given that on average, 5 pregnant women with high blood pressure come per week,

So, average = m = 5

Now, on average, 5 people come every week, so,

5 women per week,

so, we get 1 woman per (1/5)th week,

Hence, the mean is m = 1/5 for a woman arriving

and λ = 1/m = 5 = λ

we have to find the probability that it takes higher than a week for a high BP pregnant woman to arrive, i.e,

P(X>1) i.e. the probability that it takes more than a week for a high BP pregnant woman to show up,

Now,

P(X>1) = 1 - P(X<1),

Now, the probability density function is,

\(f(x) = \lambda e^{-\lambda x}\)

And the cumulative distribution function (CDF) is,

\(CDF = 1 - e^{-\lambda x}\)

Now, CDF gives the probability of an event occuring within a given time,

so, for 1 week, we have x = 1, and λ = 5, which gives,

P(X<1) = CDF,

so,

\(P(X < 1)=CDF = 1 - e^{-\lambda x}\\P(X < 1)=1-e^{-5(1)}\\P(X < 1)=1-e^{-5}\\P(X < 1) = 1 - 6.738*10^{-3}\\P(X < 1) = 0.9932\\And,\\P(X > 1) = 1 - 0.9932\\P(X > 1) = 6.8*10^{-3}\\P(X > 1) = 0.0068\)

So, the probability that on a particular week, the hospital will receive on high BP pregnant woman is 0.0068

Answer:

The inequality representing the shaded area is y < 3 - 2.5·x

Step-by-step explanation:

The given equation of the graph is 5·x + 2·y = 6

Therefore, we have;

2·y = 6 - 5·x

y = 6/2 - 5/2·x

y = 3 - 2.5·x

Given that the graph is represented by a shaded region on the left and lower side of a broken line, the inequality relationship for the graph is that of a lesser than area inequality with a symbol of < and the inequality for the graph can be represented as follows,

y < 3 - 2.5·x.

Answer:

The lengths of the sides are 20 cm and 20 cm

Step-by-step explanation:

Given

Perimeter, P = 80cm

Represent the length and width with L and W, respectively;

\(P= 2*(L + B)\)

Substitute 80 for P

\(80 = 2 * (L + B)\)

Divide through by 2

\(40 = L + B\)

\(L + B = 40\)

Make L the subject of formula

\(L = 40 - B\)

Area of a rectangle is calculated as thus;

\(Area = L * B\)

Substitute 40 - B for L

\(Area = (40 - B) * B\)

Express this as a function

\(A(B) = (40 - B)* B\)

\((40 - B)* B = A(B)\)

Set A(B) = 0 to determine the roots

Hence;

\((40 - B)* B = 0\)

\(40 - B = 0\) or \(B = 0\)

\(40 = B\) or \(B = 0\)

\(B = 40\) or \(B = 0\)

The maximum area of a rectangle occurs at half the sum of the roots;

So;

\(B= \frac{B_1 + B_2}{2}\)

\(B= \frac{40+0}{2}\)

\(B= \frac{40}{2}\)

\(B = 20\)

Recall that \(L = 40 - B\)

\(L = 40 - 20\)

\(L = 20\)

Hence the lengths of the sides are 20 cm and 20 cm

Answer:

0.167

Step-by-step explanation:

2 six sided dice= 12 total favorable outcomes

4&6= the 2 favorable outcomes

probability= fo/tfo

=2/12= 0.166666666 or 0.167

Answer:

Step-by-step explanation:

There's no image, so can't answer it.  If you upload an image, I will help :)

Answer:

Step-by-step explanation:

Need a picture or we can't solve so yes please post another one.

Nora should know that rather than inheriting longevity directly, people probably inherit risk and protective factors that influence their chances of dying earlier or later. Hence, the correct answer is option C.

The given problem here requires knowledge of both biology and mathematics in order to solve the question. The mathematical component of this question is the probability of someone inheriting logetivuty or risk factors in their life.  

The biological factor here is the inheritance of a trait. The traits in question are either longevity or risk factors. The probability of someone inheriting longevity is far less compared to the probability of inheriting a health condition that might be a risk factor for the person in the long run. Hence, option C is the correct answer.

The complete question that you might be looking for is given below-

Nora's grandfather lived to be 87, and her father is still alive at the age of 98. Nora concludes that longevity is inherited and anticipates a very long life. Nora should know that __________.

A) there is no reliable data on the heritability of longevity, so the cumulative effects of random events probably contributed to the long lives of her relatives

B) the lifespans of fraternal twins are just as similar as the lifespans of identical twins, indicating that longevity is probably not a heritable trait

C) rather than inheriting longevity directly, people probably inherit risk and protective factors that influence their chances of dying earlier or later

D) the heritability of longevity is high, ranging from .75 to .95 for age at death, indicating that longevity is directly related to genetic factors

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Answer:

C and D

Step-by-step explanation:

\(\cos(2x)\\=\cos(x+x)\\=\cos(x)\cos(x)-\sin(x)\sin(x)\\=\cos^2(x)-\sin^2(x)\\=\cos^2(x)-(1-\cos^2(x))\\=2\cos^2(x)-1 \,\,\,\,\,\,\,\,\,\,\leftarrow \text{Option D}\\=2(1-\sin^2(x))-1\\=2-2\sin^2(x)-1\\=1-2\sin^2(x)\,\,\,\,\,\,\,\,\,\,\,\leftarrow \text{Option C}\)

Answer:

it would be a closed circle and to the right

Step-by-step explanation:

I have a little tip whenever the greater or less than sign is underlined it will always be closed, and when x is greater than -4.5 all the numbers that are greater than -4.5 will be on the right side so that will be your answer.

Answer:

C=15

Step-by-step explanation:

If R=7.5 & C=2R, C=2(7.5) C=15