In a normal distribution, a data value located 1.1 standard deviations below the mean has Standard Score: z = In a normal distribution, a data value located 2.5 standard deviations above the mean has Standard Score: z = In a normal distribution, the mean has Standard Score: z =

Answer:

B, C, B, A, B

Step-by-step explanation:

Recall soh cah toa

sin - > soh     sin(ANGLE) = opposite/hypotenuse

cos -> cah     cos(ANGLE) = adjacent/hypotenuse

tan -> toa      tan(ANGLE) = opposite/adjacent  

(letters correspond)

7) They ask for sinX, meaning we need to apply soh

sinX = opposite/hypotenuse

sinX = 30/34 = 15/17

B

8)

tan(ANGLE) = opposite/adjacent  

tanZ = 12/35

C

9)

cos(ANGLE) = adjacent/hypotenuse

cosZ = 36/45 = 4/5

B

10 + 11 are attached. Hopefully, you understand. Have a nice day :)

Answer and Step-by-step explanation:

To find out how many more yards of red fabric Reuben used, we need to subtract the amount of yellow fabric from the amount of red fabric. Since the two fractions have different denominators, we need to find a common denominator before subtracting them. The least common multiple of 8 and 4 is 8, so we can rewrite both fractions with a denominator of 8:

7/8 - 1/4 = 7/8 - (1/4) * (2/2) = 7/8 - 2/8 = (7 - 2)/8 = 5/8

So, Reuben used 5/8 yards more red fabric than yellow fabric.

Answer:

Step-by-step explanation:

\(y=(\frac{1}{g} )x\)

Constant up a proportionally is  \(\frac{1}{g}\).

Answer: Number 2

Step-by-step explanation: yes

The volume of the solid obtained by rotating the region bounded by the curve y = 1 - (x - 5)² in the first quadrant about the y-axis is 51π cubic units.

To find the volume of the solid obtained by rotating the region bounded by the curve y = 1 - (x - 5)² in the first quadrant about the y-axis, we can use the method of cylindrical shells.

The formula for the volume using cylindrical shells is:

V = 2π ∫ [a, b] x * h(x) dx

Where:

- V is the volume of the solid

- π represents the mathematical constant pi

- [a, b] is the interval over which we are integrating

- x is the variable representing the x-axis

- h(x) is the height of the cylindrical shell at a given x-value

In this case, we need to solve for x in terms of y to express the equation in terms of y.

Rearranging the given equation:

x = 5 ± √(1 - y)

Since we are only interested in the region in the first quadrant, we take the positive square root:

x = 5 + √(1 - y)

Now we can rewrite the volume formula with respect to y:

V = 2π ∫ [c, d] x * h(y) dy

Where:

- [c, d] is the interval of y-values that correspond to the region in the first quadrant

To determine the interval [c, d], we set the equation equal to zero and solve for y:

1 - (x - 5)² = 0

Expanding and rearranging the equation:

(x - 5)² = 1

x - 5 = ±√1

x = 5 ± 1

Since we are only interested in the region in the first quadrant, we take the value x = 6:

x = 6

Now we can evaluate the integral to find the volume:

V = 2π ∫ [0, 1] x * h(y) dy

Where h(y) represents the height of the cylindrical shell at a given y-value.

Integrating the expression:

V = 2π ∫ [0, 1] (5 + √(1 - y)) * h(y) dy

To find h(y), we need to determine the distance between the y-axis and the curve at a given y-value. Since the curve is symmetric, h(y) is simply the x-coordinate at that point:

h(y) = 5 + √(1 - y)

Substituting this expression back into the integral:

V = 2π ∫ [0, 1] (5 + √(1 - y)) * (5 + √(1 - y)) dy

Now, we can evaluate this integral to find the volume

V = 2π ∫ [0, 1] (5 + √(1 - y)) * (5 + √(1 - y)) dy

To simplify the integral, let's expand the expression:

V = 2π ∫ [0, 1] (25 + 10√(1 - y) + 1 - y) dy

V = 2π ∫ [0, 1] (26 + 10√(1 - y) - y) dy

Now, let's integrate term by term:

\(V = 2\pi [26y + 10/3 * (1 - y)^\frac{3}{2} - 1/2 * y^2]\)] evaluated from 0 to 1

V = \(2\pi [(26 + 10/3 * (1 - 1)^\frac{3}{2} - 1/2 * 1^2) - (26 * 0 + 10/3 * (1 - 0)^\frac{3}{2} - 1/2 * 0^2)]\)

V = 2π [(26 + 0 - 1/2) - (0 + 10/3 - 0)]

V = 2π (25.5)

V = 51π cubic units

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(a) The algebraic expression, -5x - 2 + 5x + 2 is simplified as 0.

(b) The algebraic expression, 5x -2  - (5x + 2) is simplified as -4.

The given algebraic expression is simplified by adding similar terms together, as it will make the expression to be in simplest form.

The given algebraic expressions are;

-5x - 2 + 5x + 2

5x -2  - (5x + 2)

The first algebraic expression is simplified as follows;

-5x - 2 + 5x + 2

collect similar terms;

(-5x + 5x) + (-2 + 2)

= 0 + 0

= 0

The second algebraic expression is simplified as follows;

5x - 2 - (5x + 2)

= 5x - 2 - 5x - 2

collect similar terms;

= (5x - 5x) + (-2 - 2)

= 0 - 4

= - 4

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The 90% confidence interval will be (123.86,118.26)

The 95% confidence interval will be (124.4,117.72)

The probability that the parameter's true value will fall inside a given range is provided by a confidence interval. The investigator chooses the confidence level (in percentage). The confidence interval widens as the confidence level does (less precise).

One must comprehend the fundamental statistics formulas and the z-score formula before studying the confidence interval.

Given:

Sample size, n = 45

Sample mean, x' = 121.06

Standard deviation, σ = 11.43

90% confidence interval.

For a 90% confidence interval, the level of significance, α = 1 - 0.90 = 0.10

Using the z-score table, we have = 1.645

Margin of error =

E = 1.645 × σ/√n

= 1.645 ×11.43/√45

= 18.80/6.70

= 2.80

90% confidence interval =

x' ± E

= 121.06 ± 2.80

= 123.86 and 118.26

Similarly calculating z for 95% = 1.96

Now E = 3.34

95% confidence interval=

x' ± E

= 121.06 ± 3.34

= 124.4 and 117.72

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Answer:

60

Step-by-step explanation:

i did the math yeah

Answer:

C

Step-by-step explanation:

The initial value obtained using the slope-intercept relation is 3 gallons.

We need to obtain the rate of change which gives the amount of gas entering into his car per second :

Rate of change = - 11 - 3) / (48 - 0)

Rate of change = 8/48 = 1/6 gallons

Using the slope intercept relation :

Choosing any pair of (x, y) point on the table :

(0, 3)

3 = 1/6x + c

3 = 1/6(0) + c

3 = 0 + c

c = 3

Therefore, the initial value is 3 gallons.

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Using Pythagorean theorem, the length of the ladder is 10ft

In mathematical terms, if y and z are the lengths of the two shorter sides (also known as the legs) of a right triangle, and x is the length of the hypotenuse, the Pythagorean theorem can be expressed as:

x² = y² + z²

In the questions given, the only one we can use Pythagorean theorem to solve is the one with ladder since it's forms a right-angle triangle.

To calculate the length of the ladder, we can write the formula as;

x² = 8² + 6²

x² = 64 + 36

x² = 100

x = √100

x = 10

The length of the ladder is 10 feet

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Answer:

Sonya got 16 questions correct.

Step-by-step explanation:

8/10=80%

80%×20=16

(To check)

16/20=80%

The HCF of 560 and 729 is 1.

To find the HCF of 560 and 729, we use the Euclidean algorithm as follows;HCF of 560 and 729:Step 1: Divide the larger number by the smaller number, then find the remainder.729 ÷ 560 = 169 remainder 169Step 2: Divide the smaller number (i.e., 560) by the remainder (i.e., 169).560 ÷ 169 = 3 remainder 53.

Step 3: Divide the remainder from step 1 (i.e., 169) by the remainder from step 2 (i.e., 53).169 ÷ 53 = 3 remainder 10Step 4: Divide the remainder from step 2 (i.e., 53) by the remainder from step 3 (i.e., 10).53 ÷ 10 = 5 remainder 3Step 5: Divide the remainder from step 3 (i.e., 10) by the remainder from step 4 (i.e., 3).10 ÷ 3 = 3 remainder 1.

Step 6: Divide the remainder from step 4 (i.e., 3) by the remainder from step 5 (i.e., 1).3 ÷ 1 = 3 remainder 0The HCF of 560 and 729 is the last non-zero remainder, which is 1.

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The value that of the expression when n= -3 as in the task content is; Choice D; -9; First step is 3(2).

It follows from the task content that the value of the expression can be determined as follows;

n² - 3(2) + 4n

= n² - 6 + 4n

= (-3)² - 6 +4(-3)

= 9 -6 -12

= -9.

Ultimately, the first step by PEMDAS guidelines is; 3(2) and the correct choice is D.

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The probability of the event for the given odds in favor (4 to 7) is found as 4/11.

To continue solving, we must represent the ratio as a fraction.

Thus, we have the depiction shown below.

Odds ratio equals 4/7

We use the following equation to translate the aforementioned odd's expression into a probability expression.

This is displayed as

P = (Odds + 1)/(Odds).

Replace the unknown values in the equation above.

The following equation is what we have.

P = (4/7)/(4/7 + 1)

Analyze the amount

This results

P = (4/7)/(11/7)

Put the quotient in product form.

P = (4/7) * (7/11)

Evaluate

P = 4/11

Thus, the probability of event for the given odds in favor (4 to 7) is found as 4/11.

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Answer:

0.2

Step-by-step explanation:

The angle measure that belongs in the green box is given as follows:

70.67º.

We consider a triangle with side lengths and angles related as follows, as is the case for this problem:

Then the lengths and the sines of the angles are related as follows:

sin(A)/a = sin(B)/b = sin(C)/c.

The relation for this problem is given as follows:

sin(x)/12  = sin(76º)/12.34

Applying cross multiplication, the missing angle measure is given as follows:

sin(x) = 12 x sine of 76 degrees/12.34

sin(x) = 0.9436.

x = arcsin(0.9436)

x = 70.67º.

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Answer:

error in Step 2

Step-by-step explanation:

2(x - 3) + 3x = 19

Step 1 : 2x - 6 + 3x = 19 ← simplify left side by collecting like terms

Step 2 : 5x - 6 = 19 ← add 6 to both sides

Step 3 : 5x - 6 + 6 = 19 + 6

Step 4 : 5x = 25 ← divide both sides by 5

Step 5 : x = 5

Error was made by student in Step 2 who should have added 2x and 3x, not multiplied 2 × 3

Part A

The temperature of the water (in degrees Fahrenheit) after Raul added the ice cubes is 72.3 + (-39.1).

Part B

Rewrite the expression in part A by breaking up each of the place values. In this case, the place values are tens, ones, and tenths.

72.3 + (-39.1) = 70 + 2 + 0.3 + (-30) + (-9) + (-0.1)

Part C

Next, rearrange the expression in part B using the Commutative Property so the terms with the same place value are next to each other.

70 + 2 + 0.3 + (-30) + (-9) + (-0.1) = 70 + (-30) + 2 + (-9) + 0.3 + (-0.1)

Part D

Now group the terms in the expression in part C using the Associative Property.

70 + (-30) + 2 + (-9) + 0.3 + (-0.1) = [70 + (-30)] + [2 + (-9)] + [0.3 + (-0.1)]

Part E

Simplify the expression in part D to find the temperature of the water after Raul added the ice cubes. Show your work.

Part F

Several minutes later, Raul decides to measure the water temperature again. He finds that the temperature changed by -0.6°F. What is the temperature of the water now?  

The initial temperature of the water was 33.2°F. After several minutes, the temperature of the water changed by -0.6°F. So, the new temperature of the water is 33.2 + (-0.6) =

(30 + 3) + [0.2 + (-0.6)] = 33 + (-0.4) = 33 – 0.4  = 32.6°F.

Answer:

3.5841 x 10^7

Step-by-step explanation:

358.41 / 100

and add 2 powers of 10

Answer:

\(-1 \le u, v \le 1\) --- restriction

\(\sin(\cos^{-1}u + \sin^{-1}v) = \sqrt{(1 - u^2)(1 - v^2)} + uv\)

Step-by-step explanation:

Given

\(\sin(\cos^{-1}u + \sin^{-1}v)\)

Required

Write in terms of u and v

Let:

\(a =\cos^{-1}u\)

Take arc cos of both sides

\(\cos a = u\)

Using the following trigonometry identity

\(\sin^2a + \cos^2a = 1\)

So:

\(\sin^2a = 1 -\cos^2a\)

\(\sin^2a = 1 -u^2\)

Take square roots of both sides

\(\sin a = \sqrt{1 -u^2\)

So, we have:

\(\cos a = u\)     \(\sin a = \sqrt{1 -u^2\)

Let:

\(b =\cos^{-1}{\sqrt{1 - v^2}}\)

Take arc cos of both sides

\(\cos b = \sqrt{1 - v^2\)

So:

\(\sin^2b = 1 -\cos^2b\)

\(\sin^2b = 1 - (\sqrt{1 - v^2})^2\)

\(\sin^2b = 1 - (1 - v^2)\)

\(\sin^2b = 1 - 1 + v^2\)

\(\sin^2b = v^2\)

Take square roots

\(\sin b = v\)

So, we have:

\(\cos b = \sqrt{1 - v^2\)     \(\sin b = v\)

So, we have:

\(\sin(\cos^{-1}u + \sin^{-1}v)\)

\(\sin(\cos^{-1}u + \sin^{-1}v) = \sin(a + b)\)

Apply sine rule

\(\sin(\cos^{-1}u + \sin^{-1}v) = \sin a\ cos b + \sin b \cos a\)

\(\sin(\cos^{-1}u + \sin^{-1}v) = \sqrt{1 - u^2} * \sqrt{1 - v^2} + v *u\)

\(\sin(\cos^{-1}u + \sin^{-1}v) = \sqrt{(1 - u^2)*(1 - v^2)} + v *u\)

Expand

\(\sin(\cos^{-1}u + \sin^{-1}v) = \sqrt{(1 - u^2)(1 - v^2)} + uv\)

The restriction on u and v is:

\(-1 \le u, v \le 1\)

The calculated price per video game for store A is $1.79 per game

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

The price per video game for store A is calculated as

Price per video game = Total price/Number of games

using the above as a guide, we have the following:

Price per video game = 8.95/5

Evaluate the quotient

So, we have

Price per video game = 1.79

Hence, the price per video game for store A is $1.79 per game

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Answer:

d=-6.5

Step-by-step explanation:

2d+13=0

2d=-13

d= -13/2

d=-6.5

The acceleration of the car is 8 m/s^2.

The figure shown in the question is the distance-time graph of a muscle car accelerating from a standstill. The table lists the coordinates of points on the graph.The following observations can be made from the graph and the table: The car is at rest at time t=0 and at distance x=0. It then starts accelerating, and its speed increases uniformly with time. The slope of the distance-time graph is the velocity of the car.

Since the velocity is increasing uniformly, the slope of the graph is a straight line with a positive slope. The area under the graph between two points gives the displacement of the car during that time interval. The displacement can be calculated as the product of the average velocity and the time interval. Using the coordinates in the table, we can calculate the average velocities for each time interval and the displacement during that interval.

(a) The average velocity of the car between t=0 and t=2 is equal to the slope of the graph between the two points (0,0) and (2,32). This can be calculated as the difference in distance divided by the difference in time:Average velocity = (32 - 0) / (2 - 0) = 16 m/sThe displacement during this time interval is given by the area under the graph between the two points:Displacement = (1/2) x 32 x 2 = 32 m

(b) The acceleration of the car is given by the slope of the velocity-time graph. Since the velocity is increasing uniformly with time, the velocity-time graph is also a straight line with a positive slope. The slope of the velocity-time graph is equal to the acceleration. We can calculate the slope of the velocity-time graph between two points using the coordinates in the table. For example, the slope between t=0 and t=2 is given by the difference in velocity divided by the difference in time:Slope = (16 - 0) / (2 - 0) = 8 m/s^2

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Answer:

-|332|

Step-by-step explanation:

the abslute value of 332 |332| = 332

when we add minus out the abslute sign the minus will be there when we find the answer for it, so;

-|332| = -332

Answer:

I believe the answer is A. true

Answer:

True

Step-by-step explanation:

The degree 3 polynomial is "x³-2x²-64x+128".

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