The run times of a marathon runner are approximately normally distributed. The z-score for his run this week is – 2 . Which one of the following statements is a correct interpretation of his z-score?

The amount of money that is invested in the account that yields an 8% interest is $6,050.

The amount of money that is invested in the account that yields a 4% interest is $4,650.

Given these two equations:

x = y + 1400

x - y = 1400 equation 1

0.08x + 0.04y = 670 equation 2

take the following steps to determine the amount of money invested at each interest rate:

Multiply equation 1 by 0.08

0.08x - 0.08y = 112 equation 3

Subtract equation 3 from equation 2

0.12y = 558

Divide both sides by 0.12

y = 558 / 0.12

y = $4,650

x =  $4,650 + 1400

x = $6,050

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Hello!

y = 88° (opposite are equal)

z = 180° - 128° = 52° (straight angle = 180°)

x = 180° - 140° = 40° (straight angle = 180°)

Answer:

x=40°

y=88°

z=52°

Step-by-step explanation:

Solution Given:

x+140°=180°

Since the sum of the angle of a linear pair or straight line is 180°.

solving for x.

x=180°-140°

x=40°

\(\hrulefill\)

y°=88°

Since the vertically opposite angle is equal.

therefore, y=88°

\(\hrulefill\)

z+128°=180°

Since the sum of the angle of a linear pair or straight line is 180°.

solving for z.

z=180°-128°

z=52°

Answer:

As baby porcupine is backed into cactus, so the spines of cactus will feel like spines of mother porcupine. So the baby porcupine will give  call to its mother.

Step-by-step explanation

He said hi Ma.

Answer:

Perimeter is the total mesurement of all the edges of the shape. Area is the space within the perimeter,

Step-by-step explanation:

To find perimeter you add all the sides of the shape and to find area you multiply the length and the width of the shape.

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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Answer:

The probability of it landing tails on all 6 flips is 1/6 chance.

Answer:

x = 50

Step-by-step explanation:

By the definition of vertical angles you can set these two equations equal to each other.

2x+20=3(x-10)

then, just simplify to get the correct answer by using order of operations.

2x+20=3x-30

x=50

$518.5 = $375 + $41x

Now that we have our equation, let's solve for the # of hours

Subtract $375 from both sides

$143.5 = $41x

Divide both sides by $41

3.5 = x

The number of labor hours was 3.5

Answer: 1/8

Step-by-step explanation:

First make the bottom half the same:

3/4*2/2=6/8

We don’t need to change the first portion since they have a common factor

7/8-6/8=1/8

The compound inequality that represents the range of the actual weight of the object is 125.4 ≤ w ≤ 126.2.

Part A: The absolute value inequality that describes the range of the actual weight of the object is:

|w - 125.8| ≤ 0.4

Part B: To solve the absolute value inequality, we can break it down into two separate inequalities:

w - 125.8 ≤ 0.4 and - (w - 125.8) ≤ 0.4

Solving the first inequality:

w - 125.8 ≤ 0.4

Add 125.8 to both sides:

w ≤ 126.2

Solving the second inequality:

-(w - 125.8) ≤ 0.4

Multiply by -1 and distribute the negative sign:

-w + 125.8 ≤ 0.4

Subtract 125.8 from both sides:

-w ≤ -125.4

Divide by -1 (note that the inequality direction flips):

w ≥ 125.4

Combining the solutions, we have:

125.4 ≤ w ≤ 126.2

The object is 125.4 ≤ w ≤ 126.2.

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If you're looking for x, then:

2 = |x|-1

lxl-1 = 2

lxl-1+1=2+1

lxl=3

so x = -3, x=3

Answer:

6 2/3

Step-by-step explanation:

2 1/6 + 4 3/6

6 4/6

6 2/3

The three questions are illustrations of arithmetic operations and geometric progressions

(1) Acid concentration

The given parameters are:

pH of acid lemon juice = 2

pH of acid urine = 5.5

The difference between their pH is calculated as follows:

Difference = 5.5 - 2

Difference = 3.5

Multiply the difference by 10, to calculate the acidity

Acidity = 3.5 * 10

Acidity = 35

Hence, the acid like lemon juice is 35 times stronger than urine

(2) Depreciation

The depreciation is given as:

r = 18%

In 1998, the car's worth is $19995.

This is represented as:

a = 19995

2012 is 14 years from 1998.

This is represented as:

n = 14

So, the worth of the car in 2014 is calculated using:

\(\mathbf{Worth =a(1 -r)^n}\)

So, we have:

\(\mathbf{Worth =19995 \times (1 -18\%)^{14}}\)

Express percentage as decimal

\(\mathbf{Worth =19995 \times (1 -0.18)^{14}}\)

\(\mathbf{Worth =19995 \times 0.82^{14}}\)

Evaluate

\(\mathbf{Worth =1243}\)

Hence, the worth of the car in 2012 is $1243

(3) Spread of Gossip

The spread of the gossip is an illustration of geometric progression, where

a = 1 ---- the first term

r = 3 --- the common ratio

L =1200 --- the last term

So, we calculate the number of terms from 1 to 1200 using the following nth terms of geometric progression

\(\mathbf{L = ar^{n-1}}\)

This gives

\(\mathbf{1200 = 1 \times3^{n-1}}\)

\(\mathbf{1200 = 3^{n-1}}\)

Take logarithm of both sides

\(\mathbf{log(1200) = log(3^{n-1})}\)

Apply law of logarithm

\(\mathbf{log(1200) = (n-1)log(3)}\)

Divide both sides by log(3)

\(\mathbf{n - 1 = log(1200) \div log(3)}\)

\(\mathbf{n - 1 =6.45}\)

Add 1 to both sides

\(\mathbf{n =7.45}\)

Since the gossip spreads every two minutes.

The total time is:

\(\mathbf{Total =2minutes \times 7.45}\)

\(\mathbf{Total =14.9\ minutes}\)

Hence, it will take 14.9 minutes for the gossip to spread to 1200 students

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Answer: 15

Step-by-step explanation:

To solve this problem, we first need to translate the given information into a system of equations. Let's call the first number x and the second number y. Since the sum of the two numbers is 22, we know that x + y = 22.

The second statement says that three times one number increased by five is the same as twice the other number decreased by four. We can translate this into an equation by substituting x and y for the two numbers and using the given information:

3x + 5 = 2y - 4

Now that we have a system of equations, we can solve for x and y. First, we'll solve for x by adding four to both sides of the second equation:

3x + 9 = 2y

Then, we can divide both sides by three to get the value of $x$:

x = {2y - 9} / {3}

Next, we can substitute this expression for x into the first equation to solve for y:

y + {2y - 9} / {3} = 22

We can simplify this equation by multiplying both sides by three:

3y + 2y - 9 = 66

Combining like terms on the left side, we get:

5y - 9 = 66

Then, we can add nine to both sides to solve for y:

5y = 75

Finally, we can divide both sides by five to find the value of y:

y = 15

Now that we know the value of $y$, we can substitute it back into the expression for $x$ to find the value of $x$:

x = \frac{2 \cdot 15 - 9}{3} = \frac{27}{3} = 9

Since we want the larger of the two numbers, the answer is 15

The missing ordered pairs that satisfy the equation y = 2x + 4 are (3, 10) and (2, 8).

The equation given is y = 2x + 4. To compute the missing x and y values, we need to substitute the given ordered pairs into the equation and solve for the missing variable.

Let's assume we have an ordered pair (x, y) that satisfies the equation y = 2x + 4.

For example, let's say one missing value is x = 3. We can substitute this into the equation:

y = 2(3) + 4

y = 6 + 4

y = 10

So, the missing ordered pair is (3, 10).

Similarly, if another missing value is y = 8, we can substitute this into the equation and solve for x:

8 = 2x + 4

4 = 2x

x = 2

So, the missing ordered pair is (2, 8).

In summary, the missing x and y values that satisfy the equation y = 2x + 4 are (3, 10) and (2, 8).

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n⁴ - 2n³ - 23n² + 24n + 144 is the standard form of given zeroes.

What is a linear equation in mathematics?

A linear equation is an algebraic equation of the form y=mx+b. m is the slope and b is the y-intercept. The above is sometimes called a "linear equation in two variables" where y and x are variables.

                              A linear equation is an equation that raises a variable to the first power. ax+b = 0 is an example of a 1 variable. x is a variable and a and b are real numbers.  

Roots : -3(mult . 2), 4(mult.2)

the function is given as

     f(n) = (n + 3)² (n - 4)²

         = (n + 3) (n + 3 ) ( n - 4 ) ( n - 4)

        = (n² + 6n + 9) (n² - 8n + 16 )

        = n⁴ - 8n³ + 16n² + 6n³ - 48n² + 96n + 9n² - 72n + 1

collecting like term,

    f(n) = n⁴ - 2n³ - 23n² + 24n + 144

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Answer:

3zx-15z+12x-60

Step-by-step explanation:

first do parenthesis and distribute (z+4)(x-5) into zx-5z+4x-20

then distribute the 3 to get the answer

Answer:

1. 90

2. 120

3. 30

4. 60

Step-by-step explanation:

Hope it helps

Answer:

easy peasyyyyy.

1 17/24

Step-by-step explanation:

Answer:

1 17/24

Step-by-step explanation:

we have to make both denominators of the fractions the same. in order to do this you have to basically increase the fraction and make it 20/24. Do the same thing to 7/8 and get 21/24. Now we can add them together 20/24 + 21/24 = 41/24 = 1 17/24

mark me as brainliest

Answer:

If 48 adults and 26 children attended the matinee on Sunday, the theater raised $ 514 from ticket sales.

Step-by-step explanation:

A system of linear equations is a set of linear equations that have more than one unknown, which are related through the equations.

In this case, being:

The system of equations is:

\(\left \{ {{83*A+42*C=874} \atop {102*A+67*C=1151}} \right.\)

The substitution method consists of isolating one of the two unknowns in one equation to replace it in the other equation. In this case you isolate C from the first equation:

83*A + 42*C= 874

42*C= 874 - 83*A

\(C=\frac{874 - 83*A}{42}\)

Substituting this expression in the second equation:

\(102*A + 67*\frac{874 - 83*A}{42}= 1151\)

and solving:

\(102*A + \frac{67}{42} *(874 - 83*A)= 1151\)

Multiply through by 42

\(42*102*A + 42*\frac{67}{42} *(874 - 83*A)= 42*1151\)

4,284*A + 67*(874-83*A)= 48,342

4,284*A + 58,558 - 5,561*A= 48,342

4,284*A - 5,561*A= 48,342 - 58,558

-1,277*A= -10,216

\(A=\frac{-10,216}{-1,277}\)

A= 8

Knowing that: \(C=\frac{874 - 83*A}{42}\) then:

\(C=\frac{874 - 83*8}{42}\)

\(C=\frac{874 - 664}{42}\)

\(C=\frac{210}{42}\)

C= 5

The price of an adult ticket is $8 and a child is $5. If 48 adults and 26 children attended the matinee on Sunday, then:

$8*48 adults + $5* 26 childen= $514

If 48 adults and 26 children attended the matinee on Sunday, the theater raised $ 514 from ticket sales.

Answer:

P(A or B) = 0.75

Step-by-step explanation:

For Venn probabilities, we have that:

\(P(A \cup B) = P(A) + P(B) - P(A \cap B)\)

In which \(P(A \cup B)\) is P(A or B).

We have that:

\(P(A) = 0.62, P(B) = 0.25, P(A \cap B) = 0.12\)

So

\(P(A \cup B) = P(A) + P(B) - P(A \cap B) = 0.62 + 0.25 - 0.12 = 0.75\)

P(A or B) = 0.75

The probability that the song will be played on exactly 2 days out of 5 days is approximately 0.164.

To find the probability that a particular song is played exactly 2 days out of 5 days at radio station WMZH, we can use the binomial probability formula.

The binomial probability formula is given by P(x) = C(n, x) * p^x * (1-p)^(n-x), where P(x) is the probability of x successful outcomes, n is the number of trials, p is the probability of a successful outcome on a single trial, and C(n, x) represents the binomial coefficient, which is the number of ways to choose x items from a set of n items.

In this case, we want to find the probability of the song being played exactly 2 days out of 5 days, so x = 2, n = 5, and p = 3/8.

Using the formula, we have:

P(2) = \(C(5, 2) * (3/8)^2 * (1 - 3/8)^(^5^-^2^)\)

C(5, 2) = 5! / (2! * (5-2)!) = 10

P(2) = 10 * (3/8)^2 * (5/8)^3

P(2) ≈ 0.164 (rounded to three decimal places)

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Compute the partial derivatives with respect to x :

\(f(x,y)=g(y)+\tan^{-1}(xy)\)

\(\implies f_x(x,y)=\dfrac y{1+(xy)^2}\)

\(\implies f_{xx}(x,y)=-\dfrac{2xy^3}{(1+(xy)^2)^2}\)

Evaluate the second partial derivative at (2, 1) :

\(\implies f_{xx}(x,y)=\boxed{-\dfrac4{25}}\)

Answer:

sure

Step-by-step explanation:

but you gotta post the question...

Answer:

meter - yard

kilogram - 2 pounds

liter - quart

The linear function that has the same y-intercept as the given graph is the equation y = -2x + 10, corresponding to option 3.

To determine the linear function with the same y-intercept as the graph, we need to find the equation of the line passing through the points (3, 4) and (5, 0).

First, let's find the slope of the line using the formula:

slope (m) = (change in y) / (change in x)

m = (0 - 4) / (5 - 3)

m = -4 / 2

m = -2

Now that we have the slope, we can use the point-slope form of a linear equation to find the equation of the line:

y - y1 = m(x - x1)

Using the point (3, 4) as our reference point, we have:

y - 4 = -2(x - 3)

Expanding the equation:

y - 4 = -2x + 6

Simplifying:

y = -2x + 10

Now, let's check the given options to find the linear function with the same y-intercept:

Option 1: The table with x-values (-3, -1, 1, 3) and y-values (-4, 2, 8, 14)

The y-intercept is not the same as the given line. So, this option is not correct.

Option 2: The table with x-values (-4, -2, 2, 4) and y-values (-26, -18, -2, 6)

The y-intercept is not the same as the given line. So, this option is not correct.

Option 3: The table with x-values (-5, -3, 3, 5) and y-values (-15, -11, 1, 5)

The y-intercept is the same as the given line (10). So, this option is correct.

Option 4: The table with x-values (-6, -4, 4, 6) and y-values (-26, -14, 34, 46)

The y-intercept is not the same as the given line. So, this option is not correct.

Therefore, the linear function that has the same y-intercept as the given graph is the equation y = -2x + 10, corresponding to option 3.

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Answer:

Slope m= −12/5

Step-by-step explanation:

slope intercept form: y = mx + b

m = slope

b = intercept

When you have two points on the graph, plug it into x & y to find out what m (slope) and b (intercept) is.

Answer:

The value of x is 19.

Step-by-step explanation:

Given:

m∠1 = (4x + 9)°

m∠2 = (x - 14)°

Since m∠1 and m∠2 are complementary angles, we have:

m∠1 + m∠2 = 90°

Substituting the given expressions for m∠1 and m∠2:

(4x + 9)° + (x - 14)° = 90°

Combining like terms:

4x + 9 + x - 14 = 90

Combining the x terms and the constant terms:

5x - 5 = 90

Adding 5 to both sides:

5x = 90 + 5

Simplifying:

5x = 95

Dividing both sides by 5:

x = 95 / 5

Simplifying further:

x = 19

Answer:

9,10,11,12,13,14,15,16,17,18,19,20

i hope you can wrap your mind around it

enjoy your next 24 hours <3

Answer:

Step-by-step explanation:

8 učiteľov 39 študentov

1 výbor = 2 učitelia + 4 študenti

8 učiteľov :2=4

39 študentov :4= 9,75

Takže máme 4 výbory ...viacej to nemôže byť aj keď nám zostávajú študenti pretože je daný počet učiteľov...

Answer: 2303028

Step-by-step explanation: