Given that abc=def, m

Answer: 51,000 ; 111,000

Step-by-step explanation:

The formula to calculate the simple interest is: PRT/100

where,

P = principal = 60,000

R = rate = 8.5%

T = time = 10 years

Simple interest =(60000 × 8.5 × 10)/100

= 5100000/100

= 51,000

Total Amount Paid= Principal + Interest

= 60,000 + 51,000

= 111,000

Answer:

[tex] x = 5.1 yd [/tex]

Step-by-step Explanation:

Angle of depression is congruent to angle of elevation.

Therefore, angle of elevation of the given figure, which is opposite to x is 25°.

Adjacent length = 11 yd

Opposite length = x

Trigonometric ratio formula for finding x is shown below:

[tex] tan(25) = \frac{opposite}{adjacent} [/tex]

[tex] tan(25) = \frac{x}{11} [/tex]

Multiply both sides by 11 to solve for x

[tex] 11*tan(25) = x [/tex]

[tex] 5.129 = x [/tex]

[tex] x = 5.1 yd [/tex] (to the nearest tenth)

Answer:

1:3

Step-by-step explanation:

Please study the diagram briefly to understand the concept.

First, we determine the height of the isosceles trapezoid using Pythagoras theorem.

[tex]4^2=2^2+h^2\\h^2=16-4\\h^2=12\\h=\sqrt{12}\\ h=2\sqrt{3}$ units[/tex]

The two parallel sides of the trapezoid are 8 Inits and 4 units respectively.

Area of a trapezoid [tex]=\dfrac12 (a+b)h[/tex]

Area of the trapezoid

[tex]=\dfrac12 (8+4)*2\sqrt{3}\\=12\sqrt{3}$ Square Units[/tex]

For an equilateral triangle of side length s.

Area  [tex]=\dfrac{\sqrt{3}}{4}s^2[/tex]

Side Length of the smaller triangle, s= 4 Units

Therefore:

Area of the smaller triangle

[tex]=\dfrac{\sqrt{3}}{4}*4^2\\=4\sqrt{3}$ Square units[/tex]

Therefore, the ratio of the area of the smaller triangle to the area of the trapezoid

[tex]=4\sqrt{3}:12\sqrt{3}\\$Divide both sides by 4\sqrt{3}\\=1:3[/tex]

Answer:

904.32 cm^3

Step-by-step explanation:

The formula for the volume of a sphere is V=4/3πr³. Since r is given, we can plug that in for r. I'm assuming that we are using 3.14 for pi, so when we plug in all the values in the equation we get V = 4/3*3.14*6³, which solves out to 904.32.

Answer:

320793

Step-by-step explanation:

320793 / 11 = 29163

Answer:

d) Before cooling begins, the temperature of the water is 22°C

Step-by-step explanation:

Option A

If t=7 minutes

D=-7/5t+22

=-7/5(7)+22

=-49/5+22

=-49+110/5

=61/5

=12.2°C

Change in temperature=12.2°C-22°C

=-9.8°C

Option B

If t=5 minutes

D=-7/5t+22

=-7/5*5+22

=-7+22

=15°

Change in temperature=15°-22°

=-7°

Option C

The temperature of the ice must be less than 22°C

Option D

D=-7/5t+22

When ice is not placed, t=0

D=-7/5t+22

=-7/5(0)+22

=0+22

=22

Temperature of the water before cooling=22°

Answer:

D

Step-by-step explanation:

Answer: A (2,5)

Step-by-step explanation: Remove Parenthesis

                                             y = 3 (2) - 1

                                             Simplify 3 (2) - 1

                                             Multiply 3 by 2

                                             y = 6 - 1

                                             Subtract 1 from 6

                                             y = 5

Use the x and y values to from the ordered pair.

(2,5)

Answer:

(2.5)

Step-by-step explanation:

Answer:

1)2205little cherries

2)0.5.

Step-by-step explanation:

1)7little=2big

?=630big

7×630=2205little cherries

2

2)²/5x=¹/10what is the value of 10x-2

first find the value of x that is ¹/10÷²/5=¼

so x is ¼

insert the value ie 10×¼-2

=2.5-2

=0.5

Answer:

Step-by-step explanation:

E=300.

V=200.

Answer:

20°

Step-by-step explanation:

A= 360°- (160°+2*90°)= 20°

Answer:

11

Step-by-step explanation:

sub 23 with m

23 - 12 = 11

Answer: y = 2x+8

Check out this graph I supplied you with!

Answer:

( x + 36 ) ( x - 2 ) = 0

Step-by-step explanation:

x^2 + 36x - 2x -72 = 0

x ( x + 36 ) - 2 ( x + 36 ) = 0

( x + 36 ) ( x - 2 ) = 0

Answer:

only the inverse is a function

Answer:

(  3x -2)

Step-by-step explanation:

6x^2 – 7x + 2

We know that the constant only has factors of 1 and 2

Since the middle term is negative we know that that we are subtracting

A negative times a negative is positive for the final term

A negative plus a negative is negative for the middle term

(   -1 ) (   -2)

We have to determine how to break up 6x^2

1x * 6x

2x*3x

3x*2x

6x*1x

We are given that one factor is 2x-1

(  2x -1 ) (   -2)

That means the other factor of 6x^2 is 3x  ( 2x*3x)

(  2x -1 ) (  3x -2)

Answer:

3x-2

Step-by-step explanation:

Factors are:

--------------

Answer:

(Factor out 2x from the expression)

2x (x +3)

Answer:

B. 3(4 + 5) = 3(4) + 3(5)

3 left-bracket (4) (5) right-bracket = 3 (4) + 3 (5)

3 left-bracket (4) (5) right-bracket = Left-bracket 3 (4) right-bracket + Left-bracket 3 (5) Right-bracket

Step-by-step explanation:

Distributive property of multiplication over addition:

a(b + c) = ab + ac

You have

3(4 + 5), so following the pattern above, you should get:

3(4 + 5) = 3(4) + 3(5)

Answer:

b

Step-by-step explanation:

I took the test

Answer:

The data set is:

S = {4.5, 4.5, 4.5, 4.5, 6, 8, 10, 12, 13.5, 13.5, 13.5, 13.5}

Step-by-step explanation:

Consider the ordered data set:

S = {4.5, 4.5, 4.5, 4.5, 6, 8, 10, 12, 13.5, 13.5, 13.5, 13.5}

The lower extreme is: 4.5

The upper extreme is: 13.5

The median for an even number of observations is the mean of the middle two values.

[tex]\text{Median}=\frac{6^{th}+7^{th}}{2}=\frac{8+10}{2}=9[/tex]

The first quartile (Q₁) is defined as the mid-value between the minimum figure and the median of the data set.

Q₁ = 4.5

The 3rd quartile (Q₃) is the mid-value between the median and the maximum figure of the data set.

Q₃ = 13.5

A box plot that has no whiskers has, Range = Interquartile Range.

Compute the range as follows:

[tex]Rangw=Max.-Min.=13.5-4.5=9[/tex]

Compute the Interquartile Range as follows:

[tex]IQR=Q_{3}-Q_{1}=13.5-4.5=9[/tex]

Thus, the box pot for the provided data has no whiskers.

Answer: 20km/h

Step-by-step explanation:

20km/h.  Simply average 15 and 25 by doing (15+25)/2

Hope it helps <3

Answer:

Following are the answer to this question:

Step-by-step explanation:

In the question first calls the W if the transmitted chip was white so, the W' transmitted the chip is red or R if the red chip is picked by the urn II.  

whenever a red chip is chosen from urn II, then the probability to transmitters the chip in white is:  

[tex]P(\frac{w}{R}) = \frac{P(W\cap R)}{P(R)} \ \ \ \ \ _{Where}\\\\P(R) = P(W\cap R) + P(W'\cap R) \\[/tex]

The probability that only the transmitted chip is white is therefore [tex]P(W) = \frac{2}{3}\\[/tex], since urn, I comprise 3 chips and 2 chips are white.

But if the chip is white so, it is possible that urn II has 4 chips and 2 of them will be red since urn II and 2 are now visible, and it is possible to be: [tex]P(\frac{R}{W}) = \frac{2}{3}[/tex]

[tex]P(W\cap R) = P(W) \times P(\frac{R}{W}) \\[/tex]

                [tex]= \frac{2}{3}\times \frac{2}{4} \\\\= \frac{2}{3}\times \frac{1}{2} \\\\= \frac{2}{3}\times \frac{1}{1} \\\\=\frac{1}{3}\\\\= 0.333[/tex]

Likewise, the chip transmitted is presumably red [tex](P(W')= \frac{1}{3})[/tex]and the chip transferred is a red chip of urn II [tex](P(\frac{R}{W'})= \frac{3}{4}[/tex], and a red chip is likely to be red [tex](\frac{R}{W'})[/tex].  

Finally, [tex]P(W'\cap R) = P(W') \times P(\frac{R}{W'})\\[/tex]

                              [tex]= \frac{1}{3} \times \frac{3}{4} \\\\ = \frac{1}{1} \times \frac{1}{4} \\\\=\frac{1}{4}\\\\= 0.25[/tex]

The estimation of [tex]P(R)[/tex] and [tex]P(\frac{W }{R})[/tex] as:  

[tex]P(R) = 0.3333 + 0.25\\\\ \ \ \ \ \ \ \ \ \ = 0.5833 \\\\ P(\frac{W}{R}) = \frac{0.3333}{0.5833} \\\\\ \ \ \ \ \ \ = 0.5714[/tex]

Answer:

x = 50

Step-by-step explanation:

Since this is a quadrilateral, the sum is 360 degrees

2x+x+10 + 3x+x = 360

Combine like terms

7x+10 =360

Subtract 10 from each side

7x+10-10 = 360-10

7x = 350

Divide by 7

7x/7 = 350/7

x = 50

Answer:

[tex]x = 50[/tex]

Step-by-step explanation:

Sum of the interior angles in a quadrilateral

= 360°

Let's solve now

[tex]x + 10 + 3x + x + 2x = 360 \\ 7x + 10 = 360 \\ 7x = 360 - 10 \\ 7x = 350 \\ \frac{7x}{7} = \frac{350}{7} \\ x = 50[/tex]

hope this helps you.

Answer:

forty two miles over three gallons

Step-by-step explanation:

2 gallons over 32 miles simplifies to 1 gallon over 16 miles, or 1 gallon per 16 miles. This is not the desired result, so we know the first choice is incorrect.

32 miles over 2 gallons simplifies to 16 miles over 1 gallon, or 16 miles per gallon. Again, this is not the desired result, so we know the second choice is also incorrect.

3 gallons over 42 miles simplifies to 1 gallon over 14 miles, or 1 gallon per 14 miles. While this may look correct, note that 1 gallon per 14 miles and 14 miles per gallon are not the same thing, so we know that the third answer is also incorrect.

By process of elimination, we know that the correct answer must be the last option, but let's still simplify it. 42 miles over 3 gallons simplifies to 14 miles over 1 gallon, or 14 gallons per mile. This is in fact the desired result, so we know that the correct answer is the last option. Hope this helps!

[tex]\bold{\text{Answer:}\quad \text{Recursive formula:}\ a_n=a_{-1}+2n+5}\\.\qquad \qquad \ \text{Explicit formula:}\ a_n=2n^2+3n-6[/tex]

Step-by-step explanation:

-1 → 8 = +9

8 → 19 = +11

19 → 32 = +13

32 → 47 = + 15

a₁ = -1

d = 2n + 5

Recursive formula is: the previous term plus the difference (d)

                               [tex]\large\boxed{a_n=a_{n-1}+2n+5}[/tex]

Explicit formula is the first term plus the product of d and n-1:

[tex]a_n=a_1+d(n-1)\\a_n=-1+(2n+5)(n-1)\\a_n=-1+2n^2-2n+5n-5\\\large\boxed{a_n=2n^2+3n-6}[/tex]

Answer:

1) Option 2

2) Option 1

Step-by-step explanation:

1) 3a-2b

Where a = 3, b = 2

=> 3(3)-2(2)

=> 9-4

=> 5

2) 5c+3d

Where c = 4, d = -5

=> 5(4) + 3(-5)

=> 20 - 15

=> 5

Answers:

5, 5

Step-by-step explanation:

Put a as 3 and b as 2 and evaluate:

3(3) - 2(2)

9 - 4

= 5

Put c as 4 and d as -5 and evaluate:

5(4) + 3(-5)

20 - 15

= 5

Answer and Step-by-step explanation:

According to the situation, The probabilities for each one is given below:

As there are 20 families

So the probabilities for each one is

For four families have one child is

[tex]= \frac{4}{20}\\\\ = \frac{1}{5}[/tex]

For eight families have two children is

[tex]= \frac{8}{20}\\\\ = \frac{2}{5}[/tex]

For five families have three children is

[tex]= \frac{5}{20}\\\\ = \frac{1}{4}[/tex]

For two families have four children is

[tex]= \frac{2}{20}\\\\ = \frac{1}{10}[/tex]

For one family have five children is

[tex]= \frac{1}{20}[/tex]

Answer:

[tex]\boxed{Area = 3.14 ft^2}[/tex]

Step-by-step explanation:

Radius = r = 2 feet

Angle = θ = π/2 (In radians) = 1.57 radians

Area of Sector = [tex]\frac{1}{2} r^2 \theta[/tex]

Area = [tex]\frac{1}{2} (4)(1.57)[/tex]

Area = 2 * 1.57

Area = 3.14 ft²

Answer:

               [tex]\bold{2\pi\ ft^2\approx6,28\ ft^2}[/tex]

Step-by-step explanation:

360°:2 = 180° so the area of a sector bounded by a 180° arc is a half of area of a circle of the same radius.

[tex]A=\frac12\pi R^2=\frac12\pi\cdot2^2=\frac12\pi\cdot4=2\pi\ ft^2\approx2\cdot3,14=6,28\ ft^2[/tex]

Answer:

The answer is given below

Step-by-step explanation:

a) What is the probability that a randomly selected pregnancy lasts less than 242 days

First we have to calculate the z score. The z score is used to determine the measure of standard deviation by which the raw score is above or below the mean. It is given by:

[tex]z=\frac{x-\mu}{\sigma}[/tex]

Given that Mean (μ) = 247 and standard deviation (σ) = 16 days. For x < 242 days,

[tex]z=\frac{x-\mu}{\sigma}=\frac{242-247}{16}=-0.31[/tex]

From the normal distribution table, P(x < 242) = P(z < -0.3125) = 0.3783

(b) Suppose a random sample of 17 pregnancies is obtained. Describe the sampling distribution of the sample mean length of pregnancies.

If a sample of 17 pregnancies is obtained, the new mean [tex]\mu_x=\mu=247,[/tex] the new standard deviation: [tex]\sigma_x=\sigma/\sqrt{n} =16/\sqrt{17} =3.88[/tex]

c) What is the probability that a random sample of 17 pregnancies has a mean gestation period of 242 days or less

[tex]z=\frac{x-\mu}{\sigma/\sqrt{n} }=\frac{242-247}{16/\sqrt{17} }=-1.29[/tex]

From the normal distribution table, P(x < 242) = P(z < -1.29) = 0.0985

d) What is the probability that a random sample of 49 pregnancies has a mean gestation period of 242 days or less?

[tex]z=\frac{x-\mu}{\sigma/\sqrt{n} }=\frac{242-247}{16/\sqrt{49} }=-2.19[/tex]

From the normal distribution table, P(x < 242) = P(z < -2.19) = 0.0143

(e) What might you conclude if a random sample of 49 pregnancies resulted in a mean gestation period of 242 days or less?

It would be unusual if it came from mean of 247 days

f) What is the probability a random sample of size 2020 will have a mean gestation period within 11 days of the mean

For x = 236 days

[tex]z=\frac{x-\mu}{\sigma/\sqrt{n} }=\frac{236-247}{16/\sqrt{20} }=-3.07[/tex]

For x = 258 days

[tex]z=\frac{x-\mu}{\sigma/\sqrt{n} }=\frac{258-247}{16/\sqrt{20} }=3.07[/tex]

From the normal distribution table, P(236 < x < 258) = P(-3.07 < z < 3.07) = P(z < 3.07) - P(z < -3.07) =0.9985 - 0.0011 = 0.9939

Answer:

8 to the power of 1 over 3 equals 2 to the power of 3 whole to the power of 1 over 3 equals 2 to the power of 3 multiplied by 1 over 3 equals 2

Step-by-step explanation:

Options are below

8 to the power of 1 over 3 equals 4 to the power of 3 whole to the power of 1 over 3 equals 4 to the power of 3 multiplied by 1 over 3 equals 4

8 to the power of 1 over 3 equals 2 to the power of 3 whole to the power of 1 over 3 equals 2 to the power of 3 multiplied by 1 over 3 equals 2

8 to the power of 1 over 3 equals 2 to the power of 4 whole to the power of 1 over 3 equals 2 to the power of 4 multiplied by 1 over 3 equals 16

16 to the power of 1 over 4 equals 8 to the power of 2 whole to the power of 1 over 4 equals 8 to the power of 2 multiplied by 1 over 4 equals 8

Given:

8^1/3

if a power is raised to a power, we simplify it by multiplying the exponents; this will create a whole number exponent

if 8 can be rewritten as a number to the 3rd power.

We have

8 = 2*2*2 = 2³

Therefore,

8^1/3=(2^3)^1/3

=2^3×1/3

=2^3/3

=2^1

=2

Answer:

We can prove that ΔTMB ≅ ΔTMD and ΔTMA ≅ ΔTMC by ASA. This means that BM = MD = BD / 2 = 8.5 and that AM = CM = 5 which means that CD = MD - CM = 8.5 - 5 = 3.5.

Answer:

Add each given variable

(6x + 10) + (x + 2) + x = 8x + 12

The sum of all the angles equals 180ᴼ

8x + 12 = 180

Subtract 12 from both sides

8x = 168

Divide by 8 on both sides

x = 21

Now plug in 21 for each x to find the measure of each angle.

(6[21] + 10) = 126 + 10 = 136ᴼ

(21 + 2) = 23ᴼ

x = 21ᴼ