Use the table of the standard normal distribution to determine the following probabilities: a. P(0.00 < z < 2.00) b. P(0.00 < z < 1.96) c. P(z > 2.57) d. P(-2.33 < z < 2.33) e. P(z > 1.28)

Answer:

Monkey says NO

Step-by-step explanation:

Monkey says A^2 + B^2 = C^2. Monkey do math, gets C = 8.5. So close, monkey sad. Not right triangle.

Answer:

∠ AFE = 80°

Step-by-step explanation:

Since BD is a straight line , then

∠ AFB + ∠ AFE + ∠ EFD = 180°, that is

50° + ∠ AFE + 50° = 180°

100° + ∠ AFE = 180° ( subtract 100° from both sides )

∠ AFE = 80°

x = first shop

y = second shop

This year the telephone bill for the first shop was $630 less then three times the telephone bill for the second shop.

⇒ x = 3y - 630

The total telephone expense for both shops was $2446.

⇒ x + y = 2446

Solve by substitution -- the first equation into the second:

x + y = 2446 ⇒ (3y - 630) + y = 2446 ⇒ 4y = 3076 ⇒ y = $769

Substitute the value of y back into either of the original two equations to solve for x:

x = 3y - 630 ⇒ x = 3(769) - 630 = $1,677

x = $1,677

y = $769

Solution

For this case we can find the area of each triangle in the following way:

Total area is:

A= 1*1 =1

We can assume that the lenght of each side of the square is 1 then we can find the area of a like this:

a = 1/2 (1/2*1/2) = 1/8

c = 1/2 (1/2*1/2) = 1/8

We can find the area of part b like this:

b= 1/2 - 1/8 -1/8 = 1/4

We can find the proportion for the figure d like this:

d= 1/2 (1/2*1/2)= 1/8

And for the part e we can do the following:

e= 1/2 - 1/8= 3/8

Answer:

-10 is right answer

Step-by-step explanation:

see in attached picture

hope it helped you:)

Answer:

\( \frac{r}{2} + 2 = - 3\)

\( = ) \frac{r + 4}{2} = - 3\)

\( = )r + 4 = - 6\)

\( = )r \: = - 6 - 4\)

\( = )r \: = - 10\)

The relationship that describes a function is D. (appraised value, property tax).

It should be noted that a property tax simply means the tax that's paid on a property.

In this case, the relationship that describes the function is (appraised value, property tax). The variables were regarding the value of the property and the tax to be paid.

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Answer:

The length of the arc travelled by the swing is approximately 3.77 m  

Step-by-step explanation:

The given parameters of the swing are;

The swing base height of the swing above the ground = 72 cm

The swing base height above the when the swing travels an angle of 60° = 252 cm

Therefore we have;

r × cos(60°) = r - 180

180 = r - r × cos(60°)

r = 180/(1 - cos(60°)) = 360

r = 360 cm

The length of the arc travelled by the swing in meters, \(l_{arc}\) is given as follows;

\(l_{arc} = \dfrac{\theta}{360 ^{\circ}} \times \pi \times 2\times r\)

Therefore;

\(l_{arc} = \dfrac{60^{\circ}}{360 ^{\circ}} \times \pi \times 2\times360 = \dfrac{1}{6} \times \pi \times 720 = 120 \cdot \pi\)

The length of the arc travelled by the swing, \(l_{arc}\) = 120·π cm

∴ The length of the arc travelled by the swing, \(l_{arc}\) = 1.2·π m ≈ 3.77 m

A negative correlation will be expected between smoke detector use and deaths from home fires.

A positive correlation happens when variables that are related(not zero correlation)increase together. In other words, variable an (independent variable) increases and makes variable b(dependent variable) increase too.

There will be a negative correlation if the opposite happens; that is, when related variables go in opposite directions, then one of them will increase while the other decreases.

We observe from what we are told that a negative correlation occurs here since the death rate from fires has likely(assumed) decreased as smoke detectors have increased.

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--The given question is incorrect; the correct question is

"Over the past 40 years, the percentage of homes in the United States with smoke detectors has risen steadily and has plateaued at about 95% (National Fire Protection Association website, January 2015). With this increase in the use of home smoke detectors, what has happened to the death rate from home fires? The DATAfile SmokeDetectors contains 17 years of data on the estimated percentage of homes with smoke detectors and the estimated home fire deaths per million of the population.

Do you expect a positive or negative relationship between smoke detector use and deaths from home fires? Why or why not?"--

Answer: Bruce can predict the value of his investment account to be $49,800 after 3 decades

Step-by-step explanation:

If the value of the investment account doubles every decade, then after one decade (10 years), it will be worth $6,225 x 2 = $12,450.

After two decades (20 years) it will be worth $12,450 x 2 = $24,900.

Finally, after three decades (30 years), it will be worth $24,900 x 2 = $49,800.

Therefore, Bruce can predict the value of his investment account to be $49,800 after 3 decades if he makes no other deposits or withdrawals.

The correct equation representing the given translation is:

B. y = -2(x - 2) + (-2 - 3)

For a horizontal translation, we adjust the x-coordinate by adding or subtracting the desired amount. In this case, we want to move 2 units to the right, so we subtract 2 from x: (x - 2).

For a vertical translation, we adjust the y-coordinate by adding or subtracting the desired amount. In this case, we want to move 3 units downward, so we subtract 3 from y: (-2 - 3).

Combining these adjustments, we get the equation y = -2(x - 2) + (-2 - 3), which represents the given translation.

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Answer:

Multiply to remove the fraction, then set equal to 0 and solve.

Exact Form: y = − 1/10

Decimal Form: y = − 0.1

Step-by-step explanation:

Answer:

y = -1/10 or -0.1

Step-by-step explanation:

Multiply both sides of the equation by 100.

To find the opposite of 5y−17, find the opposite of each term.

The opposite of −17 is 17.

Combine 155y and −5y to get 150y.

Subtract 17 from both sides.

Subtract 17 from 2 to get −15.

Divide both sides by 150.

​Reduce the fraction  

​ to lowest terms by extracting and canceling out 15.

Therefore, in about 15 years and 2 months, the senior class will have about 100 students.

An equation is a statement that expresses the equality of two mathematical expressions using mathematical symbols such as variables, numbers, and mathematical operations. The equality is represented by an equal sign "=" between the two expressions. Equations are used to represent mathematical relationships and solve problems in various fields such as physics, chemistry, engineering, and economics.

Given by the question.

Let P be the initial population of the senior class in the high school, and r be the rate of decrease in population per year (in decimal form).

Then, we can write the following equation to represent the situation:

P\((1-r)^{n}\) = 100

We know that the current population of the senior class is 320, so we can substitute these values into the equation:

320\((1-0.07)^{n}\) = 100

Simplifying the equation, we get:

\(0.93^{n}\) = 0.3125

Taking the natural logarithm of both sides, we get:

n ln (0.93) = ln (0.3125)

Dividing both sides by ln (0.93), we get:

n = ln (0.3125) / ln (0.93)

Using a calculator, we find that n is approximately equal to 15.21 years.

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Answer:

the last one

Step-by-step explanation:

Option (B) 4 ( x + 3 ) = 32 is the equation that represents the lengths of all the worms.

We are given that:

Jeffrey has 8 worms

The 4 worms in it has the length of 3 inches.

The expression would become:

Length = 4 × 3

Also, we are given that the rest 4 worms are of equal length.

Let that equal length be x

The expression becomes:

Length = 4 × x = 4 x

Also, we are given that the total length of the worms = 32 inches.

The equation becomes:

32 = 3 × 4 + 4 × x

4 ( x + 3 ) = 32

Therefore, option (B) 4 ( x + 3 ) = 32 is the equation that represents the lengths of all the worms.

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False, every component of the matrix is multiplied by the same amount when you multiply a matrix by a number. A new matrix is created by this operation; it is known as a scalar multiple.

A rectangular matrix is a grouping of numbers in rows and columns. A matrix element/entry is the term used to describe each number in the matrix. The combination of a real number and a matrix is referred to as scalar multiplication.

Each entry/element of the matrix is multiplied by the specified scalar in scalar multiplication. Comparatively, matrix multiplication describes the result of two matrices. This operation is totally different. We can't just multiply the corresponding entries in two matrices to multiply them.

The first matrix must have exactly as many columns as the second matrix has rows in order to perform matrix multiplication. The resulting matrix has the same number of columns and rows as the second matrix, and its number of columns matches the number of rows in the first matrix.

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The probability that the date sara chose is a prime number is 0.2.

Given that, sara chose a date from the calendar.

We know that, probability of an event = Number of favourable outcomes/Total number of outcomes.

Here, total number of outcomes = 30

Number of favourable outcomes = 6

Now, probability = 6/30

= 1/5

= 0.2

Therefore, the probability that the date sara chose is a prime number is 0.2.

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Answer:

53°

Step-by-step explanation:

Let m∠BCA = 'x'

Because it states that quadrilateral ABCD is a rectangle (sorry, forgot to say that in my image), that means that angles ∠ABC, ∠BCD, ∠CDA and ∠DAB are all right angles. That also means that all those angles are 90°.

Since ∠ACD is a portion of ∠BCD, (37° is a portion of 90°), and we're looking for the complement of ∠ACD, all we have to do is subtract 37° from 90°.

90 - 37 = 53

Hence, the answer is 53°

The most probable number of hits is 4, with a probability of 0.25 or 25%.

Given that p = 0.35 and the number of shots fired is 10,

The most probable number of hits will be 10 x 0.35 = 3.5 hits.

Since we can't have half a hit, the most probable number of hits is either 3 or 4.

Using the formula above, we can find the probability of getting exactly 3 hits:

P(x = 3) = C(10,3)(0.35)3(1 - 0.35)10 - 3= 0.218

Using the formula above, we can find the probability of getting exactly 4 hits:

P(x = 4) = C(10,4)(0.35)4(1 - 0.35)10 - 4= 0.250

Therefore, the most probable number of hits is 4, with a probability of 0.25 or 25%.

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The solutions of the logarithmic equations are:

i) Ln(5x) = 7   if x = 219.32

ii) Logₓ(25) = 2    if x = 5

Here we want to solve the logarithmic equation:

Ln(5x) = 7

If we apply  the exponential function in both sides, we will get:

exp(ln5x)) = exp(7)

5x = exp(7)

x = exp(7)/5 = 219.32

The second equation is:

Logₓ(25) = 2

Remember that logₐ(x) = ln(x)/ln(a)

Then we can rewrite:

Logₓ(25) = 2

ln(25)/ln(x) = 2

ln(25)/2 = ln(x)

exp(ln(25)/2) = x

5 = x

These are the solutions.

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The diver's depth in the water at this point is 26 feet.

To determine the diver's depth in the water, we can add up the total distance he has descended and subtract the total distance he has ascended.

The diver initially descends 20 feet from the surface of the lake. Then, he rises 12 feet and descends another 18 feet.

Total descent: 20 feet + 18 feet = 38 feet

Total ascent: 12 feet

To find the diver's depth in the water, we subtract the total ascent from the total descent:

Depth in water = Total descent - Total ascent

Depth in water = 38 feet - 12 feet

Depth in water = 26 feet

Therefore, the diver's depth in the water at this point is 26 feet.

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Answer: D) 3x - 5

Step-by-step explanation:

f(x) - g(x)
f(x) = 1/2x - 3
g(x) = -5/2x + 2

Using the values of f(x) and g(x) gives us the equation:
1/2x - 3 - (-5/2x +2)

By distributing the negative sign, the signs on 5/2 and 2 are flipped, making them positive and negative respectively.

Our new equation is:

1/2x -3 + 5/2x -2
Adding up like numbers gives us:

6/2x - 5

Simplifying 6/2x => 3x

So our final equation is:

3x - 5
Hope this helps!

Answer:

Step-by-step explanation: Ok So pretend you have one apple and your friend gives you another apple how much would you have... Answer is "2"

Answer: so it is 2

Step-by-step explanation: if one friend said I have 1 bike and you said you have 1 bike that would be 2. So 1 bike + 1 bike= 2 bikes

Answer:

The answers are

→ a. 15

→ b. 27

→ c. 4

→ d. 72

→ e. 2

→ f. 9

→ g. 1

Step-by-step explanation:

Given expressions:

a. 7 + 2³

b. 9 • 3¹

c. 20 - 2⁴

d. 2 • 6²

e. 8 • (1/2)²

f. 1/3 • 3³

g. (1/5 • 5)⁵

a. 7 + 2³

\(7+2^3\)

\(2^3 = 8\)

\(8 + 7 = 15\)

Hence, 15 is your answer.

b. 9 • 3¹

\(9*3^1\)

⇒ \(9*(3)\)

⇒ \(27\)

Hence, 27 is your answer.

c. 20 - 2⁴

\(20 - 2^4\)

\(2^4 = 16\)

\(20-16 = 4\)

Hence, 4 is your answer.

d. 2 • 6²

\(2 * 6^2\)

⇒ \(2*6^2\)

⇒ \(2*(6*6)\)

⇒ \(72\)

Hence, 72 is your answer.

e. 8 • (1/2)²

\(8 * (\frac{1}{2})^2\)

⇒ \(8*((\frac{1}{2})*(\frac{1}{2}))\)

⇒ \(2\)

Hence, 2 is your answer.

f. 1/3 • 3³

\(\frac{1}{3} * 3^3\)

⇒ \(9\)

Hence, 9 is your answer.

g. (1/5 • 5)⁵

\((\frac{1}{5} * 5)^5\)

⇒ \(1*1*1*1*1\)

⇒ \(1\)

Hence, 1 is your answer.

Answer:

Alex has 3x dollars and an extra 15 dollars in his coat pocket. He buys a new Nike shoe for 84 dollars. How much money did Alex spend that was not in his pocket.

Step-by-step explanation:

Answer:

Part A: Word problem

Maria went to the store and purchased some books for her book club. Each book cost $3, and she also bought some bookmarks at $15 each. Maria's total purchase, including tax, amounted to $84. If Maria bought x books, write an equation to represent the situation.

Part B: Solution

To solve the equation 3x + 15 = 84, we need to isolate the variable x on one side of the equation.

Step 1: Subtract 15 from both sides of the equation to eliminate the constant term on the left side:

3x + 15 - 15 = 84 - 15

3x = 69

Step 2: Divide both sides of the equation by 3 to isolate x:

3x/3 = 69/3

x = 23

So, the solution to the equation is x = 23.

Part C: Explanation

In the given equation 3x + 15 = 84, the variable x represents the number of books Maria purchased. The equation states that the cost of x books at $3 each, represented by 3x, plus the cost of $15 for bookmarks, totals to $84. Thus, the value of x represents the number of books Maria bought in this scenario. In the solution, x = 23, it means Maria purchased 23 books for her book club.

Step-by-step explanation:

Hence option 1, 2, 3 are the right angle triangle.

The given triangles can be classified according to the Pythagorean theorem.

If the longest side of the triangle is c, and the other two sides are a and b, then the Pythagorean theorem states that

a² + b² = c².

1. Triangle 1: 6, 12, and 13.

The length of sides of the first triangle is 6, 12, and 13.

This triangle is a right triangle as a² + b² = c² can be applied here.

where a = 6, b = 12, and

c = 13.6² + 12²

= 36 + 144 = 18013²

= 169

Hence the triangle is a right triangle.

2. Triangle 2: 5, 12, and 13.

The length of sides of the second triangle is 5, 12, and 13.

This triangle is a right triangle as a² + b² = c² can be applied here

where a = 5, b = 12, and

c = 13.5² + 12²

= 25 + 144 = 16913²

= 169

Hence the triangle is a right triangle.

3. Triangle 3: 3, 4, and 5.

The length of sides of the third triangle is 3, 4, and 5.

This triangle is also a right triangle as a² + b² = c² can be applied here where a = 3, b = 4, and c = 5.

3² + 4² = 9 + 16 = 255² = 25.

Hence the triangle is a right triangle.

4. Triangle 4: 2, 4, and 6.

The length of sides of the fourth triangle is 2, 4, and 6.

This triangle is not a right triangle as a² + b² = c² cannot be applied here where a = 2, b = 4, and c = 6.2² + 4² = 4 + 16 = 20 (not equal to 6² = 36)

Hence the triangle is not a right triangle.

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Answer:

Answer is 628 cm^3

Step-by-step explanation:

using base area lets find radius

base area=pie*(r)^2

78.50=3.14*r^2

78.50/3.14=r^2

25=r^2

5=r

now using lateral area lets find height

lateral area=2*pie*r*h

251.20=2*3.14*5*h

251.20=31.4*h

251.20/31.4=h

8=h

volume of cylinder=pie*(r)^2*h

=3.14*(5)^2*8

3.14*25*8

=628 cm^3

Answer:

x = 12.48

Step-by-step explanation:

Simplifying

12(x + -13) = 13(12 + -1x)

Reorder the terms:

12(-13 + x) = 13(12 + -1x)

(-13 * 12 + x * 12) = 13(12 + -1x)

(-156 + 12x) = 13(12 + -1x)

-156 + 12x = (12 * 13 + -1x * 13)

-156 + 12x = (156 + -13x)

Solving

-156 + 12x = 156 + -13x

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '13x' to each side of the equation.

-156 + 12x + 13x = 156 + -13x + 13x

Combine like terms: 12x + 13x = 25x

-156 + 25x = 156 + -13x + 13x

Combine like terms: -13x + 13x = 0

-156 + 25x = 156 + 0

-156 + 25x = 156

Add '156' to each side of the equation.

-156 + 156 + 25x = 156 + 156

Combine like terms: -156 + 156 = 0

0 + 25x = 156 + 156

25x = 156 + 156

Combine like terms: 156 + 156 = 312

25x = 312

Divide each side by '25'.

x = 12.48

Simplifying

x = 12.48

Answer:

x=72±2180313=72±21803√13

Step-by-step explanation:

Answer:

0

Step-by-step explanation:

8+56/-7x-4

8+(-8)x-4

0x-4

0

Hope this helps ;) ❤❤❤

Answer:

-38

Step-by-step explanation:

4-(3^4-6^2)+2(3)÷2

=>     4 - (81-36) + 2(3) ÷ 2      

=>     4 -  45 + 2(3)÷2

=>     4 -  45 + 6÷2

=>     4 -   45 + 3

=>     -41 + 3

=>     - 38

hope this helps :)