Look at this equation.
0.3x + 5. 14 = 2. 1x - 4.4
Which value of x makes the equation true?
0
-5.3
O - 4.1
O 4.1
O 5.3

Mrs. Grubbs would get more cookie to eat by choosing the 4 smaller cookies with diameter 5 cm each rather than the single cookie with diameter 14 cm.

To compare the amount of cookie Mrs. Grubbs would get by eating a single cookie with diameter 14 cm and 4 smaller cookies with diameter 5 cm each, we need to consider the total area of the cookies.

The area of a cookie with diameter 14 cm can be calculated as follows:

A = πr^2 = π(7 cm)^2 = 49π cm^2

where r is the radius of the cookie.

On the other hand, the area of a single small cookie can be calculated as follows:

A1 = \(πr^2\) = \(π(2.5 cm)^2\)= \(6.25π cm^2\)

where r is the radius of the small cookie.

Therefore, the total area of 4 small cookies is:

A2 = 4A1 = \(4(6.25π cm^2)\) = \(25π cm^2\)

Comparing the two options, we see that the total area of the 4 small cookies is greater than the area of the single large cookie:

A2 > A

\(25π cm^2 > 49π cm^2\)

It's worth noting that this comparison assumes that the thickness or volume of the cookies is the same for both options. If the cookies have different thicknesses, then the comparison would need to take into account the volume of the cookies instead of just the area.

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Answer:

Below

Step-by-step explanation:

The equation to use for CONTINUOUS compounding is :

FV = PV e^(it)

18532.08 = 8327 * e^( i*10)        where i is the interest in decimal form

18532.08/8327  = e^(10i)

2.225541 = e^(10i)             now take natural log  (ln) of both sides to get

.8000 = 10i

i = .08     or 8% interest

The probability that the student got an 'A' given they are male is approximately 0.12 or 12%.

To find the probability that a student got an 'A' given they are male, we need to use Bayes' theorem:

P(A | Male) = P(Male | A) × P(A) / P(Male)

We can find the values of the terms in the formula using the information given in the table:

P(Male) = (25/54) = 0.46 (the proportion of all students who are male)

P(A) = (17/54) = 0.31 (the proportion of all students who got an 'A')

P(Male | A) = (3/17) = 0.18 (the proportion of all students who are male and got an 'A')

Therefore, plugging these values into the formula:

P(A | Male) = 0.18 × 0.31 / 0.46

P(A | Male) ≈ 0.12

So the probability that the student got an 'A' given they are male is approximately 0.12 or 12%.

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Answer:

where is the pic? please give it

Answer:

Where is the question lol

Answer:

Step-by-step explanation:

8C2  * 6C2

============

14C4

8C2 = 8*7/1 * 2 = 28

6C2 = 6*5 / 1*2 = 15

14C4 = 14*13 *12 * 11 / (1 * 2 * 3 * 4) = 1001

28 * 15 / 1001 = .4195

Answer:

hope it may help you

Step-by-step explanation:

n and n+14 are the numbers or you can use n and n-14; either way

n+n+14=58

2n+14=58

2n=58-14

2n=44

n=22 and n+14=22+14=36

22 and 36 are the numbers

or,...

58/2=29

29 and 29

28 and 30

27 and 31

26 and 32

25 and 33

24 and 34

23 and 35

22 and 36 answer

Answer:

-8

Step-by-step explanation:

3-11=-8

Answer:

8

Step-by-step explanation:

The temperature at the bottom of the mountain is 50.9 °C.

Let's work through the given information step by step to find the temperature at the bottom of the mountain.

The temperature in the hotel is 21 °C.

The temperature in the hotel is 26.7 °C warmer than at the top of the mountain.

Let's denote the temperature at the top of the mountain as T_top.

So, the temperature in the hotel can be expressed as T_top + 26.7 °C.

The temperature at the top of the mountain is 3.2 °C colder than at the bottom of the mountain.

Let's denote the temperature at the bottom of the mountain as T_bottom.

So, the temperature at the top of the mountain can be expressed as T_bottom - 3.2 °C.

Now, let's combine the information we have:

T_top + 26.7 °C = T_bottom - 3.2 °C

To find the temperature at the bottom of the mountain (T_bottom), we need to isolate it on one side of the equation. Let's do the calculations:

T_bottom = T_top + 26.7 °C + 3.2 °C

T_bottom = T_top + 29.9 °C

Since we know that the temperature in the hotel is 21 °C, we can substitute T_top with 21 °C:

T_bottom = 21 °C + 29.9 °C

T_bottom = 50.9 °C

Therefore, the temperature at the bottom of the mountain is 50.9 °C.

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The output voltage of an amplifier is 1350mV.

The voltage that a machine, like a voltage regulator or a generator, releases into the air is known as the output voltage. Voltage regulators keep voltage levels steady.

Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.

Given that the output voltage of an amplifier is calculated by multiplying the input voltage by the voltage gain of the amplifier.

The output voltage will be calculated as:-

Output voltage = 45 x 30

Output voltage = 1350 mV

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Answer:

.1

Step-by-step explanation:

Answer:

Point Q is represented by the ordered pair (-2,9)

Answer

2

Step-by-step explanation:

1 + 1 =2

Finn would run 18 miles after 6 track practices.

We have,

Generally, A unit rate is a ratio of two measurements with a denominator of 1. To find the number of miles Finn would run after 6 track practices, we can use the unit rate of miles per practice to multiply by the number of practices.

Unit rate: 6 miles / 2 practices = 3 miles per practice

To find the total number of miles Finn would run after 6 practices, we can multiply the unit rate of 3 miles per practice by the number of practices, 6.

Total miles: 3 miles/practice * 6 practices = 18 miles

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Answer:

a) r(t) = (10, 5, -5) + (5, 5, 0)*t

b) (0, -5, -5)

Step-by-step explanation:

a) 2x + 4 -2y -5 = -3z -6

2x - 2y +3z +5 =0

(10, 5, -5)

(15, 10, -5)

(5, 5, 0)

r = (10, 5, -5) + (5, 5, 0)*t

b) The yz plane is given by the equation x = 0.

x = 0  in the vector equation of a straight line if and only if  t = -2, than r ( - 2) = (0, -5, -5) is the desired intersection point.

Answer: your answer should be 103

The largest N such that the probability that there are at least N survivors at age 95 is at least 90% is approximately 136.43.

The normal approximation can be used to estimate the number of survivors at a given age when the mortality follows the Standard Ultimate Life Table. The normal approximation assumes that the number of survivors follows a normal distribution.

Let X be the number of survivors at age 95. Then, the mean (μ) and standard deviation (σ) of X can be calculated using the following formula:

μ = 4,000 * e⁽⁻⁰.⁰⁷³⁶⁽⁹⁵⁻²⁵⁾⁾

σ = √(4,000 * (1 - e⁽⁻⁰.⁰⁷³⁶⁽⁹⁵⁻²⁵⁾⁾) * e⁽⁻⁰.⁰⁷³⁶⁽⁹⁵⁻²⁵⁾⁾)

Next, we can find the value of N such that P(X >= N) >= 0.9 using the standard normal distribution.

z = (N - μ) / σ

P(X >= N) = 1 - P(X < N) = 1 - Φ(z)

where Φ(z) is the cumulative distribution function of the standard normal distribution.

We want to find the largest N such that P(X >= N) >= 0.9, so we need to find the smallest z such that Φ(z) <= 0.1. The value of z can be found using a standard normal table or a calculator with normal distribution functions.

With a calculator, we get that z = 1.28. So, N = μ + z * σ.

Plugging in the values we calculated earlier, we get:

N = 4,000 * e⁽⁻⁰.⁰⁷³⁶⁽⁹⁵⁻²⁵⁾⁾ + 1.28 * √(4,000 * (1 - e⁽⁻⁰.⁰⁷³⁶⁽⁹⁵⁻²⁵⁾⁾) * e⁽⁻⁰.⁰⁷³⁶⁽⁹⁵⁻²⁵⁾⁾)

N = 4,000 * e⁽⁻⁰.⁰⁷³⁶⁽⁷⁰⁾⁾ + 1.28 * √(4,000 * (1 - e^⁽⁻⁰.⁰⁷³⁶⁽⁷⁰⁾) * e^⁽⁻⁰.⁰⁷³⁶⁽⁷⁰⁾⁾

N = 4,000 * 0.0337 + 1.28 * √(4,000 * (1 - 0.0337) * 0.0337)

N = 132.8 + 1.28 * √(4,000 * 0.966 * 0.0337)

N = 132.8 + 1.28 * √(13.97376)

N = 132.8 + 3.63323

N ≈ 136.43

So, the largest N such that the probability that there are at least N survivors at age 95 is at least 90% is approximately 136.43.

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The length of side AB is about 5.87 units.

The triangle ABC is a right angle triangle. A right angle triangle is a triangle that has one of its angles as 90 degrees.

Therefore, let's find the length AB in the right triangle.

Using trigonometric ratios,

cos 33 = adjacent / hypotenuse

Therefore,

Adjacent side = AB

hypotenuse side = 7 units

cos 33° = AB / 7

cross multiply

AB = 7 cos 33

AB = 7 × 0.83867056794

AB = 5.87069397562

AB = 5.87 units

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Answer:

Step-by-step explanation:

This problem has been solved! You'll get a detailed solution from a subject matter expert that helps you learn core concepts.

Answer:

  4

Step-by-step explanation:

You want to know what number, multiplied by (5 +6), gives 20 +24.

For some number 'a', you want ...

  a(5 +6) = (20 +24)

We can solve for 'a' in the usual way.

  11a = 44 . . . . simplify

  a = 44/11 = 4 . . . . divide by the coefficient of 'a'

The missing number is 4: 4(5 +6) = 20 +24.

__

Additional comment

You can also look at it term by term:

  5a = 20   ⇒   a = 4

  6a = 24   ⇒   a = 4 . . . . the same factor, as you want it to be

1. The function f that determines the height of the beanstalk is \(h(t) = 7 * (1.15)^t\)

2. f(1)/f(0) = 1.15.

3. f(2)/f(1) = 1.149.

Let h be the height of the beanstalk in inches after t days. Then we can write: \(h(t) = 7 * (1.15)^t\) where 1.15 is the factor by which the height increases each day.

i. To compute f(1)/f(0), we need to substitute t = 1 and t = 0 into the function f and divide:

f(1)/f(0) = [7 * (1.15)^1] / [7 * (1.15)^0]

f(1)/f(0) = 1.15/1

f(1)/f(0) = 1.15

ii. To compute f(2)/f(1), we need to substitute t = 2 and t = 1 into the function f and divide:

f(2)/f(1) = [7 * (1.15)^2] / [7 * (1.15)^1]

f(2)/f(1)= (1.3225) / (1.15)

f(2)/f(1) = 1.149

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To find the distance between points A and B, we can use trigonometry and the given information.

Let's label the distance between A and B as "d". We know that point C is 94.4 meters away from point A. From angle A, we have the measure of 72°, and from angle C, we have the measure of 30°.

Using trigonometry, we can use the tangent function to find the value of "d".

tan(72°) = d / 94.4

To solve for "d", we can rearrange the equation:

d = tan(72°) * 94.4

Using a calculator, we can evaluate the expression:

d ≈ 4.345 * 94.4

d ≈ 408.932

Therefore, the distance between points A and B is approximately 408.932 meters.

Answer:

j is -18

Step-by-step explanation:

\( - 108pi = 6pij \\ - 108 = 6j \\ j = - 18\)

The solution is j = -18 for the expression -108π = 6πj

Arithmetic operations can also be specified by subtracting, dividing, and multiplying built-in functions.

The operator that performs the arithmetic operations is called the arithmetic operator.

Operators who let do basic mathematical calculations.

- Subtraction operation: Subtracts the right-hand operand from the left-hand operand.

for example 4 -2 = 2

* Multiplication operation: Multiplies values on either side of the operator

For example 4*2 = 8

Given that the expression

⇒ -108π = 6πj

Divided by 6π both sides

⇒ -108π/6π  = 6πj/6π  

⇒ -18  = j  

⇒ j = -18

Thus, the solution is j = -18 for the expression -108π = 6πj

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Answer:

2.8

Step-by-step explanation:

2.8*10=28

Also, when you multiply 2.8 by 10, you can just move the decimal to the right once, giving you 28.

Answer:

$40.34

Step-by-step explanation:

x+(x+.91)=81.59

2x+.91=81.59

2x=80.68

x=40.34

Answer:

1. Triangles HIJ and KML

2. Triangles RST and YXZ

3. Reflexive property and Congruent Property

Step-by-step explanation:

Step-by-step explanation:

for 1 and 2 to find which ones are congruent you have to look at the lines on the angles which show congruence

Similarity statement and justification for two similar figures with given measurements. The given figures are AB = 40, AC = 50, and BC = 60. For the second figure, YX = 37.5, YZ = 30, and ZX = 45.

To write a similarity statement, we compare the ratios of corresponding sides of the two figures. So, we can compare AB/BC to YX/ZX and AC/BC to YZ/ZX.AB/BC = 40/60 = 2/3YX/ZX = 37.5/45 = 5/6AC/BC = 50/60 = 5/6YZ/ZX = 30/45 = 2/3Since the ratios of the corresponding sides of both figures are the same, we can say that the two figures are similar.

A similarity statement for these figures can be written as:ΔABC ~ ΔXYZThis statement indicates that the two triangles ABC and XYZ are similar. The symbol ~ is used to denote similarity.

The justification for this similarity statement is based on the fact that the ratios of the corresponding sides of the two figures are equal.

Therefore, by the definition of similarity, we can conclude that the two triangles are similar.

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Answer:

Step-by-step explanation:

3t-9<6

3t<6+9

or 3t<15

or t<5

-3t<12

-t<4

or t>-4

or -4<t

combining

-4<t<5

The value of t for the inequalities are,

1)  t < 5

2) t > - 4

A relation by which we can compare two or more mathematical expression is called an inequality.

Given that;

The inequality are,

⇒ 3t - 9 < 6

⇒ - 3t < 12

Now, Simplify the inequality for t as;

1) ⇒ 3t - 9 < 6

Add 9,

⇒ 3t - 9 + 9 < 6 + 9

⇒ 3t < 15

Divide by 3;

⇒ t < 5

2) - 3t < 12

⇒ - 3t < 12

Divide by 3;

⇒ - t < 12/3

⇒ - t < 4

Multiply by - 1,

⇒ t > - 4

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Given

Total number of members = 22

Find

Possible ways of selection of president, a secretary and a treasurer

Explanation

As we know , the number of possible ways of selection is given by

there are three members required so , r = 3

now , substitute the values in above equation

Final Answer

Possible ways of selection of president, a secretary and a treasurer = 9240

Answer:

C.

Step-by-step explanation:

It is not a straight line therefore it cannot be linear.

Answer:

f(x) = x³ - 4x + 6

f'(x) = 3x² - 4

a) f'(2) = 3(2²) - 4 = 12 - 4 = 8

6 = 8(2) + b

6 = 16 + b

b = -10

y = 8x - 10

b) 3x² - 4 = 0

3x² = 4, so x = ±2/√3 = ±(2/3)√3

= ±1.1547

f(-(2/3)√3) = 9.0792

f((2/3)√3) = 2.9208

c) 3x² - 4 = 8

3x² = 12

x² = 4, so x = ±2

f(-2) = (-2)³ - 4(-2) + 6 = -8 + 8 + 6 = 6

6 = -2(8) + b

6 = -16 + b

b = 22

y = 8x + 22

f(2) = 6

y = 8x - 10

The equation perpendicular to the tangent is y = -1/8x + 25/4

-The smallest slope on the curve is 2.92

The curve has the smallest slope at the point (1.15, 2.92)

The equations at tangent points are y = 8x + 16 and  y = 8x - 16

From the question, we have the following parameters that can be used in our computation:

y = x³ - 4x + 6

Differentiate

So, we have

f'(x) = 3x² - 4

The point is (2, 6)

So, we have

f'(2) = 3(2)² - 4

f'(2) = 8

The slope of the perpendicular line is

Slope = -1/8

So, we have

y = -1/8(x - 2) + 6

y = -1/8x + 25/4

We have

f'(x) = 3x² - 4

Set to 0

3x² - 4 = 0

Solve for x

x = √[4/3]

x = 1.15

So, we have

Smallest slope = (√[4/3])³ - 4(√[4/3]) + 6

Smallest slope = 2.92

So, the smallest slope is 2.92 at (1.15, 2.92)

Here, we set f'(x) to 8

3x² - 4 = 8

Solve for x

x = ±2

Calculate y at x = ±2

y = (-2)³ - 4(-2) + 6 = 6: (-2, 0)

y = (2)³ - 4(2) + 6 = 6: (2, 0)

The equations at these points are

y = 8x + 16

y = 8x - 16

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