Simplify using the Distributive Property.
7 × 48
A. (7 × 50) − (7 × 2) = 350 – 14 = 336
B. (7 × 40) + 8 = 288
C. (7 × 50) – 2 = 348
D. (7 × 40) + (7 x 8) + 7 = 343

Answer:

x^2 - 5x - 66

Step-by-step explanation:

1. Distrubute the x to the x and -11 so you will get x^2 - 11x

2. Distrubute the 6 to x and -11 and you get 6x - 66

3. Combine like terms (x^2 - 11x + 6x - 66) you will get x^2 - 5x - 66

To find the probability distribution for Y, the number of errors detected by the auditor, we can use the binomial distribution formula. The binomial distribution is used when there are only two possible outcomes, success or failure, and each trial is independent.

In this case, the probability of success (detecting an error) is 5% or 0.05, and the probability of failure (not detecting an error) is 1 - 0.05 = 0.95.

a. To find the probability distribution for Y, we can use the formula for the binomial distribution:

P(Y = y) = (nCk) * p^k * (1-p)^(n-k)

where n is the number of trials (3 in this case), k is the number of successes (errors detected), p is the probability of success (0.05), and (nCk) is the combination formula.

For y = 0:
P(Y = 0) = (3C0) * (0.05)^0 * (0.95)^(3-0) = (1) * (1) * (0.95)^3 = 0.857375

For y = 1:
P(Y = 1) = (3C1) * (0.05)^1 * (0.95)^(3-1) = (3) * (0.05) * (0.95)^2 = 0.135375

For y = 2:
P(Y = 2) = (3C2) * (0.05)^2 * (0.95)^(3-2) = (3) * (0.05)^2 * (0.95)^1 = 0.007125

For y = 3:
P(Y = 3) = (3C3) * (0.05)^3 * (0.95)^(3-3) = (1) * (0.05)^3 * (0.95)^0 = 0.000125

So the probability distribution for Y is:
Y = 0 with probability 0.857375
Y = 1 with probability 0.135375
Y = 2 with probability 0.007125
Y = 3 with probability 0.000125

b. To construct a probability histogram for p(y), you can create a bar graph where the x-axis represents the number of errors detected (Y) and the y-axis represents the probability (P(Y = y)). Each bar will have a height corresponding to the probability.

c. To find the probability that the auditor will detect more than one error, we need to calculate the sum of the probabilities for Y = 2 and Y = 3:

P(Y > 1) = P(Y = 2) + P(Y = 3) = 0.007125 + 0.000125 = 0.00725

Therefore, the probability that the auditor will detect more than one error is 0.00725.

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the answer is c (x=15)...

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We can expect that out of 50 draws with replacement, approximately 25 blue marbles will be chosen on average.

If the probability of drawing a blue marble from the bag is 1/2, and the marble is replaced after each draw, we can expect that the probability of drawing a blue marble remains constant for each draw. Therefore, for each individual draw, there is a 1/2 chance of selecting a blue marble.

To predict how many times a blue marble will be chosen out of 50 draws, we can use the concept of expected value. The expected value is calculated by multiplying the probability of an event by the number of times it is expected to occur.

In this case, the probability of drawing a blue marble is 1/2 for each draw, and we are drawing 50 times. Therefore, the expected number of blue marbles drawn can be calculated as:

Expected number of blue marbles = Probability of drawing blue × Number of draws

= (1/2) × 50

= 25

Based on this calculation, we can expect that out of 50 draws with replacement, approximately 25 blue marbles will be chosen on average.

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Based on the text, the primary source of primate endangerment today is habitat destruction.

Habitat destruction is considered the primary source of primate endangerment based on various factors mentioned in the text. Primates, like many other species, heavily rely on their natural habitats for survival, including food, shelter, and breeding. However, human activities such as deforestation, urbanization, and land conversion for agriculture or infrastructure development have significantly reduced and fragmented primate habitats.

Habitat destruction leads to the loss of critical resources and disrupts the ecological balance necessary for primate populations to thrive. As their habitats shrink, primates face increased competition for limited resources, reduced access to food and water sources, and decreased opportunities for successful reproduction and rearing of offspring. This loss of habitat also exposes primates to increased vulnerability to predation, disease transmission, and human-wildlife conflicts.

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Answer:

30 because negative x negative = a positive number

The formula to find the distance between a point and a line is

Graphically

So, in this case, you have

Then

The absolute value is the distance between a number and zero. The distance between -10 and 0 is 10.

Therefore, the distance between the point of the line is 10 units.

The global maximum value is 44, and the global minimum value is -88.

To determine the global extreme values of the function f(x, y) = 11x - 5y subject to the given constraints, we need to analyze the function within the feasible region defined by the inequalities.

First, let's consider the boundary of the feasible region:

For x ≥ -8 and y ≥ x - 8, we have y ≥ -8 and y ≥ -x - 8. The feasible region is defined by the intersection of these two inequalities, which is a triangle with vertices (-8, -8), (-8, 0), and (0, -8).

For x ≤ 4 and y ≤ 4, we have y ≤ 4. The feasible region is the triangle with vertices (4, 4), (4, 0), and (0, 4).

Now, we need to evaluate the function at the vertices of the feasible region:

f(-8, -8) = 11(-8) - 5(-8) = -88 + 40 = -48

f(-8, 0) = 11(-8) - 5(0) = -88

f(0, -8) = 11(0) - 5(-8) = 40

f(4, 4) = 11(4) - 5(4) = 44 - 20 = 24

f(4, 0) = 11(4) - 5(0) = 44

From these evaluations, we can see that the maximum value of the function is 44, which occurs at the point (4, 0), and the minimum value is -88, which occurs at the point (-8, -8).

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Answer:

360 polygon

Step-by-step explanation:

follow me and mark this answer

Answer:

The answer is 84.

Step-by-step explanation:

The given equation is

4x*2 + 2x -5 = 0

Here a= 4, b= 2, c= -5

Since Discriminant= b*2 -4ac

Putting values

Discriminant= (2)*2 - 4(4)(-5)

= 4 + 80

= 84

Since our Discriminant(84) is >0 and is not a perfect square so the roots of the given equation are unequal and irrational(real).

the equivalent expression is:

60*x^8

Which is option B.

Here we start with:

4*x^2*√(5x^4)*3*√(5x^8)

Remember that square roots are distributive, then we can just write:

(4*3)*(x^2)*(√(5x^4)*√(5x^8))

12*x^2*√(25x^12)

Now, the square root can now be solved

12*x^2*√(25x^12) = 12*x^2*5*x^6

= (12*6)*(x^2*x^6)

Remember that in the right side, the exponents just add, then we get:

(12*6)*(x^2*x^6) = 60*x^{2 + 6} = 60*x^8

Then the equivalent expression is:

60*x^8

Which is option B.

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The quadratic function graphed is defined as follows:

g(x) = -4(x - 1)² + 3.

The quadratic function of vertex(h,k) is given by the rule presented as follows:

y = a(x - h)² + k

In which:

The coordinates of the vertex in this problem are given as follows:

(1,3).

Hence:

g(x) = a(x - 1)² +  3.

When x = 2, g(x) = -1, hence the leading coefficient a is obtained as follows:

-1 = a + 3

a = -4.

Hence the function is:

g(x) = -4(x - 1)² + 3.

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Answer:

All your definitions are right. I gave examples for each example

The probability of two events happening one after another is the product of both probabilities.

The probability of winning at the machine X is 12/100 and the probability of winning at the machine Y is 7/100. Then, the probability of winning at both playing once at each machine, is:

On the other hand, since the probability of winning at machine X is 12/100, then the probability of loosing is 88/100. Similarly, the probability of loosing at machine Y is 93/100. Then, the probability of loosing at both machines is:

Therefore, the probability of winning at both machines is 0.84% and the probability of loosing at both machines is 81.84%.

3(2x - 4) = 6(x + 2)

The equation that has no solution is the one that leads to a contradiction, where the left side of the equation does not equal the right side regardless of the value of x.

Let's analyze the given equations:

Ix - 3r-4=4

Zx - 3r+4=4

3(2x - 4) = 6(x^2)

3(2x - 4) = 6(x + 2)

Upon evaluating these equations, it is evident that equation 3 is not possible because it simplifies to 6x - 12 = 6x^2, which is a quadratic equation. However, there is no value of x that satisfies this equation, leading to a contradiction. Therefore, the equation 3(2x - 4) = 6(x^2) has no solution.

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Answer:75.708L

Step-by-step explanation:

Answer:

y = - 5/3x + 1

Step-by-step explanation:

Slope of line j = (-2-4)/(-5-5)

Slope = -6/-10 = 3/5

Slope of the perpendicular line k: -5/3

Point of line k: (-3,6)

y-intercept of line k = 6 - (-5/3)(-3) = 6 - 5 = 1

Answer:

It is A

Step-by-step explanation:

You have 4 muffins or 4m with a 2 dollar off coupon so therefore it is 4m-2

Answer:

4m-2

Step-by-step explanation:

The cost, m, is subtracted by 2. There are 4 muffins being bought, so the term would be 4m, making the equation 4m-2.

Answer:

No because cuboid a is smaller than cuboid b

Step-by-step explanation:

Answer:

No.

Step-by-step explanation:

They do not have the same surface area. My calculations as to how I know: A = 2x2x2+3x2x2+3x2x2= 4x2+6x2+6x2= 8+12+12= 20+12= 30cm B = 1x3x2 + 1x4x2 + 3x4x2= 3x2 + 4x2 + 12x2= 6+8+24 14+24= 38cm

By the information provided in the question, we got to know that - there are 2598960 ways.

Combining means selecting all or part of a set of objects, regardless of the order in which the objects are selected. Suppose we have a set of three characters.

\(^nC_{r} = \frac{n!}{r!(n - r)!}\)

You are choosing a subset of size 5 from a set of size 52.

\(Note that the order you are dealt these 5 cards is irrelevant.\) Thus, order doesn’t matter.

Thus, this is a combination problem. The formula for this is:

\(Comb(52,5) = \frac{52!}{5! 13!} = 2598960.\)

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Solution

For Logan

Principal (P) = $8,100

Rate (R) = 5%

Time (T) = 4 years

The Interest

The balance in logan account will be

The amount is $9,720

For Rita

Note: Compound Interest Formula

Using the above formula, we have

The balance in Rita account is $9,845.60 (to two decimal places)

Therefore, the difference in their account balances is

Therefore the answer is $125.60

Answer:

y=3

Step-by-step explanation:

as perpendicular to y axis so it means parallel to x-axis and we measure slope with positive x axis

The probability density function (pdf) of the largest of the five waiting times is given by: f(x) = 4/10^5 * x^4, where x is a real number between 0 and 10. The expected value of the largest of the five waiting times is 8.33 minutes.

The pdf of the largest of the five waiting times can be found by considering the order statistics of the waiting times. The order statistics are the values of the waiting times sorted from smallest to largest.

In this case, the order statistics are X1, X2, X3, X4, and X5. The largest of the five waiting times is X5.

The pdf of X5 can be found by considering the cumulative distribution function (cdf) of X5. The cdf of X5 is given by: F(x) = (x/10)^5

where x is a real number between 0 and 10. The pdf of X5 can be found by differentiating the cdf of X5. This gives: f(x) = 4/10^5 * x^4

The expected value of X5 can be found by integrating the pdf of X5 from 0 to 10. This gives: E[X5] = ∫_0^10 4/10^5 * x^4 dx = 8.33

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Putting it all together, we get:

A:

[-3 0 0]

[ 0 1 0]

[ 0 0 -1]

which is an orthogonal matrix with the first row being a multiple of (3, 3, 0).

An orthogonal matrix is a square matrix whose columns and rows are orthonormal vectors, i.e., each column and row has unit length and is orthogonal to the other columns and rows.

Let's start by finding a vector that is orthogonal to (3, 3, 0). We can take the cross product of (3, 3, 0) and (0, 0, 1) to get such a vector:

(3, 3, 0) x (0, 0, 1) = (3*(-1), 3*(0), 3*(0)) = (-3, 0, 0)

Note that this vector has length 3, so we can divide it by 3 to get a unit vector:

(-3/3, 0/3, 0/3) = (-1, 0, 0)

So, the first row of the orthogonal matrix A can be (-3, 0, 0) or a multiple of it. For simplicity, we'll take it to be (-3, 0, 0).

To find the remaining two rows, we need to find two more orthonormal vectors that are orthogonal to each other and to (-3, 0, 0). One way to do this is to use the Gram-Schmidt process.

Let's start with the vector (0, 1, 0). We subtract its projection onto (-3, 0, 0) to get a vector that is orthogonal to (-3, 0, 0):

v1 = (0, 1, 0) - ((0, 1, 0) dot (-3, 0, 0)) / ||(-3, 0, 0)||^2 * (-3, 0, 0)

= (0, 1, 0) - 0 / 9 * (-3, 0, 0)

= (0, 1, 0)

We can then normalize this vector to get a unit vector:

v1' = (0, 1, 0) / ||(0, 1, 0)|| = (0, 1, 0)

So, the second row of the orthogonal matrix A is (0, 1, 0).

To find the third row, we take the cross product of (-3, 0, 0) and (0, 1, 0) to get a vector that is orthogonal to both:

(-3, 0, 0) x (0, 1, 0) = (0, 0, -3)

We normalize this vector to get a unit vector:

v2' = (0, 0, -3) / ||(0, 0, -3)|| = (0, 0, -1)

So, the third row of the orthogonal matrix A is (0, 0, -1).

Putting it all together, we get:

A:

[-3 0 0]

[ 0 1 0]

[ 0 0 -1]

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The value of c that satisfies the equation  \(\sum_{n=1}^{\infty} e^{nc}=10\)  is approximately -0.0451.

What is a equation?

An equation is a mathematical statement that asserts the equality of two expressions.

To find the value of c such that the infinite series \(\sum_{n=1}^{\infty} e^{nc}\) is equal to 10, we can use the formula for the sum of an infinite geometric series with \(a = e^c\).

The formula for the sum of an infinite geometric series is given by:

S = a / (1 - r),

where S is the sum of the series, a is the first term, and r is the common ratio.

In this case, \(a = e^c\) and the common ratio \(r = e^c\).

We can rewrite the equation as:

\(10 = e^c / (1 - e^c)\)

Next, let's solve for c:

\(10(1 - e^c) = e^c\)

\(10 - 10e^c = e^c\)

\(10 = 11e^c\)

\(e^c = 10 / 11\)

Taking the natural logarithm (ln) of both sides:

\(c = ln(10 / 11)\)

Using a calculator, we can find the approximate value of c:

c ≈ -0.0451.

Therefore, the value of c that satisfies the equation  \(\sum_{n=1}^{\infty} e^{nc}=10\)  is approximately -0.0451.

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Answer:

h = 20 mean h can only be 20

h < 20 means h can only be a number that is smaller than 20, can't be exactly 20

Step-by-step explanation:

h = 20

This means the variable h can only be 20; it can't be lower or higher than 20.

h < 20

This means the variable h can only be smaller than 20; this means the number can only be below 20 and can't be exactly 20.

only Marina with 16 cases of diet soda is a valid answer, as it results in a whole number of cases. Therefore, Marina completed the task correctly

In mathematics, natural numbers are employed for count and ranking. Ordinal numbers are used for organisation, while cardinal numbers are used for counting.

To count or sort them, use the zeros  and on and on. An integer sum is one that is made up of only integers. not utilising fractions or decimals. Decimals or fractions are not what integers are.

Although there is only one type of integer Not all integers too are integers or unnatural numbers (just as all of them are natural numbers). For instance, the number -5 is neither a natural number nor an integer, but both.

Based on the given information, we know that the ratio of regular soda to diet soda being shipped is 8:3. We can use this ratio to find the number of cases of diet soda for each student who completed the task correctly.

Let's calculate the number of cases of diet soda for each student:

Barrie: 27

Number of cases of diet soda = 27 * 3/8 = 10.125 (rounded to the nearest whole number) - This is not a valid answer as the number of cases of diet soda should be a whole number.

Marina: 16

Number of cases of diet soda = 16 * 3/8 = 6

Jordan: 36

Number of cases of diet soda = 36 * 3/8 = 13.5 (rounded to the nearest whole number) - This is not a valid answer as the number of cases of diet soda should be a whole number.

Hai: 20

Number of cases of diet soda = 20 * 3/8 = 7.5 (rounded to the nearest whole number) - This is not a valid answer as the number of cases of diet soda should be a whole number.

Valerie: 11

Number of cases of diet soda = 11 * 3/8 = 4.125 (rounded to the nearest whole number) - This is not a valid answer as the number of cases of diet soda should be a whole number.

Coleman: 51

Number of cases of diet soda = 51 * 3/8 = 19.125 (rounded to the nearest whole number) - This is not a valid answer as the number of cases of diet soda should be a whole number.

Based on the calculations, only Marina with 16 cases of diet soda is a valid answer, as it results in a whole number of cases. Therefore, Marina completed the task correctly.

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The best representation of the inequality y ≤ - 5/6x + 2/3 is shown in figure by red shade region.

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

We have to given that;

The inequality is,

⇒ y ≤ - 5/6x + 2/3

Now, We can draw the graph of inequality y ≤ - 5/6x + 2/3.

Hence, The best representation of the inequality y ≤ - 5/6x + 2/3 is shown in figure by red shade region.

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