simplify the expression
algebra 2 high school math part 2 ​

(a) P(z < -0.83) = 0.7967

(b) P(z > 1.07) = 0.1423

(c) If P(z > a) = 0.2033, then a = 0.84

To find the probabilities using the ∠-table (cumulative probabilities under the standard normal distribution), follow these steps:

(a) P(z < -0.83):

Look up the value -0.8 in the leftmost column of the table and the value 0.03 in the top row. The corresponding value in the table is 0.2033. Since the table provides values for positive z-scores, we can use the symmetry property of the standard normal distribution to find the desired probability:

P(z < -0.83) = 1 - P(z < 0.83) = 1 - 0.2033 = 0.7967

(b) P(z > 1.07):

Look up the value 1.0 in the leftmost column of the table and the value 0.07 in the top row. The corresponding value in the table is 0.8577. Since the table provides values for positive z-scores, we need to find the complement of the desired probability:

P(z > 1.07) = 1 - P(z < 1.07) = 1 - 0.8577 = 0.1423

(c) If P(z > a) = 0.2033, find the value of a:

Using the table, we find that the closest value to 0.2033 in the table is 0.20, which corresponds to a z-score of -0.84. Since we are interested in the upper tail, the desired value of a is the negative of the z-score:

a = -(-0.84) = 0.84

Therefore, the answers are:

(a) P(z < -0.83) = 0.7967

(b) P(z > 1.07) = 0.1423

(c) If P(z > a) = 0.2033, then a = 0.84

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Answer:

9 or +9

Step-by-step explanation:

The main level would be 0. Any level below that would be -1, -2 etc.

Answer: It is A hope this helps :)

Step-by-step explanation:

To solve the equation and find the radius, we need to rewrite it in the form of a circle equation, which is (x - h)² + (y - k)² = r², where (h, k) represents the center of the circle and r represents the radius.

Given equation: x² + y² + 2x - 10y + 8 = 8y - 46

To rewrite the equation in the form (x - h)² + (y - k)² = r², we complete the square for both the x and y terms:

[tex]\sf\:(x^2 + 2x) + (y^2 + 10y) = 8y - 46 - 8 \\[/tex]

Completing the square for x terms:

[tex]\sf\:x^2 + 2x = (x + 1)^2 - 1 \\[/tex]

Completing the square for y terms:

[tex]\sf\:y^2 + 10y = (y + 5)^2 - 25 \\[/tex]

Substituting the completed square forms into the equation:

[tex]\sf\:(x + 1)^2 - 1 + (y + 5)^2 - 25 + 8 = 8y - 46 - 8 \\[/tex]

Simplifying the equation:

[tex]\sf\:(x + 1)^2 + (y + 5)^2 = 8y - 46 - 8 + 1 + 25 - 8 \\[/tex]

[tex]\sf\:(x + 1)^2 + (y + 5)^2 = 8y - 36 \\[/tex]

Now we can see that the equation is in the form of (x - h)² + (y - k)² = r², where h = -1, k = -5, and r² = 8y - 36. Therefore, the radius is [tex]\sf\:\sqrt{8y - 36} \\[/tex].

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♥️ [tex]\large{\textcolor{red}{\underline{\mathcal{SUMIT\:\:ROY\:\:(:\:\:}}}}[/tex]

Answer:

7 cups of water

Step-by-step explanation:

Divide 56 by 24

56/24 = 2 1/3

Multiply this by the cups of water wasted every 24 hrs

2 1/3 x 3 = 7

Answer:

32600000

Step-by-step explanation:

= 3.26 × 107

(scientific notation)

= 3.26e7

(scientific e notation)

= 32.6 × 106

(engineering notation)

(million; prefix mega- (M))

= 32600000

(real number)

The future value of the $10,000 investment after 7 years, at an interest rate of 6% per year, compounded annually, is approximately $14,185.10.

To calculate the future value (FV) of an investment of $10,000 at an interest rate of 6% per year, compounded annually, after 7 years, we can use the formula:

FV = P(1 + r)^n

Where:

P is the principal amount (initial investment) = $10,000

r is the interest rate per period = 6% = 0.06

n is the number of periods = 7

Plugging in the values, we have:

FV = $10,000(1 + 0.06)^7

Calculating the expression inside the parentheses first:

(1 + 0.06)^7 ≈ 1.41851

Now, multiply the principal amount by the calculated expression:

FV ≈ $10,000 * 1.41851 ≈ $14,185.10

Therefore, the future value of the $10,000 investment after 7 years, at an interest rate of 6% per year, compounded annually, is approximately $14,185.10.

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Answer:

Step-by-step explanation:

1.

[tex] \frac{15}{3} + 2 = 15 \div (3 + 2) \\ 5 + 2 = 15 \div 5 \\ 7 = 3 \\ false[/tex]

2.

[tex] \frac{15}{3 + 2} = 15 \div 5 \\ \frac{15}{5} = 15 \div 5 \\ 3 = 3 \\ true[/tex]

Answer:

1.) a= -49

2.) t= 3

Step-by-step explanation:

Based on the evidence from the given sample, we have sufficient evidence to refute the claim that the mean is 40 with a standard deviation of 15.

To determine whether the evidence refutes the claim that the mean is 40 with a standard deviation of 15, we can perform a hypothesis test using the given sample mean and the claimed mean.

Let's set up the null and alternative hypotheses:

Null hypothesis (H0): The mean is equal to 40 (µ = 40).

Alternative hypothesis (HA): The mean is not equal to 40 (µ ≠ 40).

We can use a t-test to compare the sample mean to the claimed mean. Given that we have a sample size of 100, we can assume the sample mean follows an approximately normal distribution due to the Central Limit Theorem.

The test statistic for this scenario is the t-score, which measures the difference between the sample mean and the claimed mean in terms of standard errors.

The formula for the t-score is:

t = (sample mean - claimed mean) / (sample standard deviation / sqrt(sample size))

Using the given information, we can calculate the t-score:

t = (35.8 - 40) / (15 / sqrt(100))

t = -4.2 / (15 / 10)

t = -4.2 / 1.5

t = -2.8

Next, we need to compare the t-score with the critical value at a given significance level (e.g., α = 0.05) and the degrees of freedom (df = n - 1 = 100 - 1 = 99).

Using a t-table or statistical software, we can find the critical values for a two-tailed test with a significance level of 0.05 and 99 degrees of freedom. The critical t-values are approximately -1.984 and 1.984.

Since the calculated t-score (-2.8) is outside the range of the critical values (-1.984 to 1.984), we reject the null hypothesis.

Therefore, based on the evidence from the given sample, we have sufficient evidence to refute the claim that the mean is 40 with a standard deviation of 15.

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Answer:

[tex]d=8.9[/tex]

Step-by-step explanation:

Distance Formula: [tex]d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]

Simply plug in the 2 coordinates into the distance formula to find distance d:

[tex]d=\sqrt{(4-0)^2+(-4-4)^2}[/tex]

[tex]d=\sqrt{(4)^2+(-8)^2}[/tex]

[tex]d=\sqrt{16+64}[/tex]

[tex]d=\sqrt{80}[/tex]

[tex]d=4\sqrt{5}[/tex]

[tex]d=8.94427[/tex]

[tex]d=8.9[/tex]

Answer:

Your answer is: No solution

Step-by-step explanation:

Hope this helped : )

Answer:neither are functions

Step-by-step explanation:

Functions don't have repeated x

Answer:

30

Step-by-step explanation:

1. x + 40 = 3x - 20

2. 40 = 2x - 20

3. 60 = 2x

4. 30 = x

Answer:

300

Step-by-step explanation:

225 is what you start with. 15 liter per min means in 5 min it will be 75 because 5x15=75, then 75+225=300

Answer:

The answer is

[tex]x^2 = 6y[/tex]

Step-by-step explanation:

Answer:

21 bags. 1 Jolly rancher in each bag and 2 tootsie rolls on each bag.

Answer:

Para las siguientes fórmulas se tiene la siguiente notación:

\displaystyle I : Interés

\displaystyle C : Capital inicial

\displaystyle i : Tasa de interés

\displaystyle t : Tiempo

\displaystyle F : Capital final (o valor futuro)

Así, las fórmulas relacionadas con el cálculo de interés simple, cuando la tasa de interés y el tiempo utilizan la misma unidad de tiempo, son:

\displaystyle  I= C \cdot t \cdot i

\displaystyle  t=\frac{I}{C \cdot i}

\displaystyle C=\frac{I}{t \cdot i}

\displaystyle  i=\frac{I}{C \cdot t}

\displaystyle  F = C+I

Notemos que si el tiempo y el interés utilizan unidades distintas, entonces tendremos que hacer las conversiones apropiadas antes de utilizar las fórmulas.

Ejercicios propuestos de calculo de intéres

1 ¿Durante cuánto tiempo ha de imponerse un capital de 25 000 € al 5% para que se convierta en 30.000 €?

Solución

2 Se prestan 45 000 € y al cabo de un año, 4 meses y 15 días se reciben 52 500 €.

Calcular el interés como porcentaje.

Solución

3 Hallar la tasa de interés simple (como porcentaje) al que deberá prestarse un capital para que al cabo de 20 años los intereses sean equivalentes al capital prestado.

Solución

4 ¿En cuánto tiempo el interés será igual al triple del capital inicial colocado a una tasa de interés al 6%?

Solución

5 Hallar el interés producido durante cinco años, por un capital de 30 000 €, al 6%.

Solución

6 Calcula el capital final después de seis meses, dado un capital inicial de 10 000 € y una tasa del 3.5%

The expression that simplifies to 2/15 is 4/30.

Option C is the correct answer.

We have,

To find the expression that simplifies to 2/15, we need to simplify each option and see which one equals 2/15.

Let's simplify each option:

A) 4/17: This expression cannot be simplified further. It does not equal 2/15.

B) 6/19: This expression cannot be simplified further. It does not equal 2/15.

C) 4/30: We can simplify this expression by dividing both the numerator and denominator by their greatest common divisor, which is 2. Simplifying gives us 2/15, so option C equals 2/15.

D) 12/60: We can also simplify this expression by dividing both the numerator and denominator by their greatest common divisor, which is 12. Simplifying gives us 1/5, not 2/15.

Therefore,

The expression that simplifies to 2/15 is 4/30.

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The complete question:

Which expression simplifies to 2/15 ??

A 4/17

B 6/19

C 4/30

D 12/60

a. (0,0), (5,0), (3.75, 3.75), (3.5,4.5), (0,8);

b. x = 3.5, y = 4.5, OFV = 59.5;

c. s1 = 0, s2 = 2, s3 = 0.

a. The extreme points of the feasible region are the vertices of the polygon formed by the intersection of the constraint lines. In this case, the extreme points are (0,0), (5,0), (3.75, 3.75), (3.5,4.5), and (0,8).

b. To find the optimal solution and the objective function value, we evaluate the objective function at each extreme point and choose the point that maximizes the objective function. In this case, the point (3.5, 4.5) maximizes the objective function with a value of 59.5. Therefore, the optimal solution is x = 3.5 and y = 4.5, and the objective function value is 59.5.

c. The slack variables represent the surplus or slack in each constraint. We calculate the slack variables by subtracting the actual value of the left-hand side of each constraint from the right-hand side. In this case, the values of the slack variables are s1 = 0 (indicating no slack in the first constraint), s2 = 2 (indicating a surplus of 2 in the second constraint), and s3 = 0 (indicating no slack in the third constraint).

Therefore, the correct option is:

a. (0,0), (5,0), (3.75, 3.75), (3.5,4.5), (0,8);

b. x = 3.5, y = 4.5, OFV = 59.5;

c. s1 = 0, s2 = 2, s3 = 0.

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Answer:

2

Step-by-step explanation:

-3x+5 = 2<5

two less than 5

Answer:

35

Step-by-step explanation:

4 times 8 +3=35

Answer:

C

Step-by-step explanation:

I think that the planets will keep orbiting the sun but i think the planets might cross paths with the new star.

Answer:

24, 36, 48, and 60

Step-by-step explanation:

The data chosen when using a Systemic Sampling Technique has a specific set interval which keeps on repeating itself until all the data has been chosen. Therefore since the first number that was selected from the population was 12, we can assume that the selected numbers will be every 12 digits. Therefore based on this information, we can calculate that the next four numbers that are chosen would be the 24, 36, 48, and 60

Answer: x=8

Step-by-step explanation:

15*8 = 120 + 20 = 140

140+40 = 180 a perfect line

Answer:

Below

Step-by-step explanation:

Angle on a straight line =180

[tex]40\° + (15x +20)\°=180\°\\\\40 \°+(15(8)+20)\° =180\°\\\\40\°+(120+20)\°=180\°\\\\40\°+140\°=180\°\\\\180\°=180\°[/tex]

In a binomial experiment with n trials and probability of success p, if n is large and/or p is close to 0.5, the binomial random variable X is approximately normal with μX = np and σX = sqrt(np(1-p)).

In a binomial experiment with n trials and probability of success p, if n is large and/or p is close to 0.5, the binomial random variable X is approximately normal with μX = np and σX = sqrt(np(1-p)). A binomial experiment involves a fixed number of independent trials (n) each having the same probability of success (p).The binomial distribution is a discrete probability distribution that describes the probability of success in a binomial experiment. When the sample size is large, the binomial distribution may be approximated by the normal distribution.This is because the normal distribution is continuous, whereas the binomial distribution is discrete. If the sample size is large enough, the binomial distribution can be well approximated by the normal distribution. For this approximation to work well, n should be large and p should be close to 0.5.When the binomial distribution is approximated by the normal distribution, the mean of the binomial distribution, which is np, is also the mean of the normal distribution. The standard deviation of the normal distribution is the square root of np(1-p).

In summary, when n is large and/or p is close to 0.5, the binomial random variable X is approximately normal with μX = np and σX = sqrt(np(1-p)).

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Answer:

B

Step-by-step explanation:

point-slope form is y-y1=m(x-x1)

x1=-3

y1=-1

m=2

Now plug it in!

y-(-1)=2(x-(-3))

Simplify it to

y+1=2(x+3)

Therefore, it should be B

Hope this helps!

Since the exponential function is always positive, there is no solution for e^(-2t) = -1/6. This means that the derivative is never equal to zero, and there is no point of maximum steepness for this curve.

To find the point at which the curve is steepest, we need to find the maximum value of the derivative of the function. Let's start by finding the derivative of the given function:

y = 50 / (1 + 6e^(-2t))

To find the derivative, we can use the quotient rule:

y' = [50(0) - (1 + 6e^(-2t))(-12e^(-2t))]/(1 + 6e^(-2t))^2

Simplifying this expression, we get:

y' = (72e^(-2t))/(1 + 6e^(-2t))^2

To find the maximum point, we need to find the value of t for which the derivative is equal to 0. Setting y' = 0 and solving for t, we have:

(72e^(-2t))/(1 + 6e^(-2t))^2 = 0

Since the numerator cannot be zero, we focus on the denominator:

(1 + 6e^(-2t))^2 = 0

Taking the square root of both sides, we get:

1 + 6e^(-2t) = 0

Solving for e^(-2t), we have:

e^(-2t) = -1/6

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Answer:

2/5 or 2 over 5

Step-by-step explanation:

y2-y1 over x2-x1 gives you your slope