(Factoring Algebraic Expressions MC)

There are 9,000 numbers that have 7 in the thousands of places and are less than 54,000.

Consider the possible digits in the hundreds, tens, and one's places.

Thousands of places: There is only one possibility, which is 7.

Hundreds place: Any digit from 0 to 9 is possible.

Tens place: Any digit from 0 to 9 is possible.

One place: Any digit from 0 to 9 is possible.

Since the number is less than 54,000, the digit in the hundreds place cannot be 5.

So, there are 9 possible digits (0 to 9, except 5) for the hundreds place, and 10 possible digits (0 to 9) for the tens and one's places.

So, the total number of such numbers is:

9 x 10 x 10 x 10 = 9,000

Therefore, there are 9,000 numbers that satisfy the given condition.

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The probability of one defective compressor among the first 6 examined, the probability of four or more defective compressors among the first 6 examined, and the probability of 1 to 3 defective compressors among the first 6 examined are 0.1136, 0.1212, and 0.7955 respectively.

(a) .1136, .1212 and 0.7955 respectively.

(i) P(X=1) = C(5,1) / C(12,6) = 5/66 = 0.1136

(ii) P(X ≥ 4) = P(X = 4) + P(X = 5) + P(X = 6) = C(5,4) / C(12,6) + C(5,5) / C(12,6) + C(5,6) / C(12,6) = .1212

(iii) P(1≤X ≤3) = P(X = 1) + P(X = 2) + P(X = 3) = C(5,1) / C(12,6) + C(5,2) / C(12,6) + C(5,3) / C(12,6) = 0.7955

The probability of one defective compressor among the first 6 examined is P(X = 1) = C(5,1) / C(12,6) = 5/66 = 0.1136. The probability of four or more defective compressors among the first 6 examined is P(X ≥ 4) = P(X = 4) + P(X = 5) + P(X = 6) = C(5,4) / C(12,6) + C(5,5) / C(12,6) + C(5,6) / C(12,6) = .1212. The probability of 1 to 3 defective compressors among the first 6 examined is P(1≤X ≤3) = P(X = 1) + P(X = 2) + P(X = 3) = C(5,1) / C(12,6) + C(5,2) / C(12,6) + C(5,3) / C(12,6) = 0.7955.

Therefore, the probability of one defective compressor among the first 6 examined, the probability of four or more defective compressors among the first 6 examined, and the probability of 1 to 3 defective compressors among the first 6 examined are 0.1136, 0.1212, and 0.7955 respectively.

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It’s cAnswer:

Step-by-step explanation:

it’s right

The graph that represents the situation is added as an attachment

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

This means that the graph would be represented using a distance/time graph

Such that the distance would be on the y-axis and the time would be on the x-axis

See attachment for the graph

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Answer: A. Job A pays more

B. $49.80

Step-by-step explanation:

Answer: \(y=-\frac{7}{4}x-\frac{3}{4}\)

Step-by-step explanation:

Rearranging the line into slope-intercept form,

\(4y+7x=-6\\\\4y=-7x-6\\\\y=-\frac{7}{4}x-\frac{3}{2}\)

Since the center of dilation does not lie on the line, we can multiply the y-intercept by the scale factor of the dilation.

So, the equation of the line is \(y=-\frac{7}{4}x-\frac{3}{4}\)

Answer:

0.5 ㏑ | 1-2x | +c

Step-by-step explanation:

Formula:  ∫ 1/ax+b dx = 1/a ln Iax+bI +c

Answer:

the answer is 2

Step-by-step explanation:

just plug in the 3 for x and perform the neccessary calculation.

Answer:

2

Step-by-step explanation:

if x is 2 that means 2 + 3 = 5

Give me brainllest Plz

Answer:

The rates are not equivalent since Maria saves $0.50 more per month than Ralph.

Step-by-step explanation:

We can determine if two rates are equivalent by comparing the rates at which they save per month.

Maria's savings per month:

Both 50 and 4 can be divided by 2, which gives us 25/2.  As a regular number, this becomes 12.5/1 which means Maria saves $12.5 per month.

Ralph's savings per month:

Both 60 and 5 can be divided by 5, which gives us 12.  Thus, Ralph saves $12 per month.

Thus, the rates are not equivalent as Maria saves $0.50 more per month than Ralph.

300 with a remainder of 10

3 0 0

1 4 | 4 2 1 0

4 2

1 0

Therefore, 4210 / 14 = 300 with a remainder of 10.

300 with a remainder of 10

Answer:

Step-by-step explanation:

4×1½×2 = 4×3 = 12

The maximum and minimum points of the function are (a) (3π/2, -1) (-π/2, -1), (π/2, 3)

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

y = –2 cos (x + π/2) + 1.

Calculating the maximum

Here, we have

y = –2 cos (x + π/2) + 1.

Next, we plot the graph of the function

From the graph of the function, we have the maximum points to be (π/2, 3)

Calculating the minimum

Here, we have

y = –2 cos (x + π/2) + 1.

Next, we plot the graph of the function

From the graph of the function, we have the minimum points to be

(3π/2, -1) (-π/2, -1)

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Answer:

he will eat 35/64  of the whole pie

Step-by-step explanation:

i hope i helped

The sequence that shows the numbers in order from least to greatest is D. 2.14 < 2.8 < 3.16227766017.

The sequence that shows the numbers in order from least to greatest is D. 2.14 < 2.8 < 3.16227766017.What is the meaning of the inequality symbols?The inequality symbols are mathematical symbols that are used to compare two values.

They indicate the relationship between two values that are not equal to each other. Here are the inequality symbols:

< (less than)≤ (less than or equal to)> (greater than)≥ (greater than or equal to)What is the meaning of the sequence?

A sequence is a set of numbers arranged in a particular order. The order of the numbers in a sequence can be from smallest to largest or largest to smallest.

The sequence D. 2.14 < 2.8 < 3.16227766017 is arranged from smallest to largest because the first number in the sequence, 2.14, is the smallest, and the last number in the sequence, 3.16227766017, is the largest.

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The method that will not give the correct number of inches is that the total length of the plant in a week is 19/4 inches.

Length of the small plant = 2 1/2 = 5/2 inches

Rate of growth = 3/4 inches

Increase in length in 3 weeks will be:

= 3 × 3/4 = 4

Total length = 5/2 + 9/4

= 19/4 inches.

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Answer:

45 times

Explanation:

A six-sided number cube has the following numbers written on its six faces.

1, 2, 3, 4, 5, 6

As can be seen, three of the above numbers (1, 3 and 5) are odd. This means that half of the cube faces have odd numbers printed on them.

Therefore, the probability that a toss would land on an odd number is 1/2 or 50%.

Now if we do 90 tosses, then we expect that 50% of them would give us an odd number.

Therefore, the number of tosses we expect to give an odd number is

Hence, we expect the number cube to give us odd numbers 45 times out of 90 tosses.

Answer:

For acute angles, remember what sine means: opposite over hypotenuse. If we increase the angle, then the opposite side gets larger. That means "opposite/hypotenuse" gets larger or increases.

Step by Step:

Keep this in mind >>

Consider the unit circle > The sine and cosine ratios are the only ratios that have 1 (the radius or hypotenuse) as the denominator. The numerators (sides) vary between 0 and 1, thus determining that the sine and cosine do the same.

All of the other ratios (tangent, cotangent, secant, cosecant) have a side as the denominator, varying between 0 and 1. As any denominator approaches 0, the value of the ratio approaches infinity.

1. The function f that determines the height of the beanstalk is \(h(t) = 7 * (1.15)^t\)

2. f(1)/f(0) = 1.15.

3. f(2)/f(1) = 1.149.

Let h be the height of the beanstalk in inches after t days. Then we can write: \(h(t) = 7 * (1.15)^t\) where 1.15 is the factor by which the height increases each day.

i. To compute f(1)/f(0), we need to substitute t = 1 and t = 0 into the function f and divide:

f(1)/f(0) = [7 * (1.15)^1] / [7 * (1.15)^0]

f(1)/f(0) = 1.15/1

f(1)/f(0) = 1.15

ii. To compute f(2)/f(1), we need to substitute t = 2 and t = 1 into the function f and divide:

f(2)/f(1) = [7 * (1.15)^2] / [7 * (1.15)^1]

f(2)/f(1)= (1.3225) / (1.15)

f(2)/f(1) = 1.149

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Answer:true

Step-by-step explanation:because yes

Answer:

The answer is below

Step-by-step explanation:

The equation of a linear function is given as:

y = mx + b;

where y, x are variables, m is the rate of change and b is the initial value of variable y.

A) Since there is B bacteria in the Petri dish at 12:00 midnight and the number of bacteria increases after midnight by 25 every hour. Let h represent the time in hours and T represent the total number of bacteria, therefore the equation is:

T = 25h + B

B) Given that B = 5, h = 6, hence:

T = 25(6) + 5 = 150 + 5 = 155 bacteria

C) The equation of the graph is:

T = 25h + 5

The graph was plotted using geogebra online graphing.

Answer:

The coefficient of \(x^{4}\)\(y^{3}\) is -280

Step-by-step explanation:

Solving the Binomial expansion using the Pascal's triangle, it would be observed that an expansion to the power of 7 can be solved using;

1  7  21  35  35  21  7  1

Thus;

\((x - 2y)^{7}\) = 1. \(x^{7}\) + 7.\(x^{6}\)(-2y) + 21.\(x^{5}\)\((-2y)^{2}\) + 35.\(x^{4}\)\((-2y)^{3}\) + 35.\(x^{3}\)\((-2y)^{4}\) + 21.\(x^{2}\)\((-2y)^{5}\) + 7.x\((-2y)^{6}\) + \((-2y)^{7}\)

        = \(x^{7}\) -14\(x^{6}\)y +84\(x^{5}\)\(y^{2}\) -280\(x^{4}\)\(y^{3}\) + 560\(x^{3}\)\(y^{4}\) - 672\(x^{2}\)\(y^{5}\) + + 448x\(y^{6}\) - 128\(y^{7}\)

Therefore, the coefficient of \(x^{4}\)\(y^{3}\) is -280

Answer:

n = \(\frac{d-4m}{7}\)

Step-by-step explanation:

Given

d = 4m + 7n ( subtract 4m from both sides )

d - 4m = 7n ( isolate n by dividing both sides by 7 )

\(\frac{d-4m}{7}\) = n

Answer:

n = d - 4m ÷ 7

Step-by-step explanation:

d = 4m + 7n

d - 4m = 7n

7n = d - 4m

n = d - 4m ÷ 7

Thus, n = d - 4m ÷ 7

-TheUnknownScientist

Answer:

d) 19.8 lb

Step-by-step explanation:

1 lb = 0.454 kg

9 kg * (1 lb)/(0.454 kg) = 19.8 lb

\(-\frac{10}{3}=-3.\overline{3} > -3.\overline{5}\)

So, the answer is A.

Answer:

-5/4x + 3

Step-by-step explanation:

Answer:

D. \(10^{\circ}\)

Step-by-step explanation:

Let the measure of minor arc \(AE\) be \(\alpha\) and the measure of minor arc \(BD\) be \(\beta\).

Using the secant-secant theorem, \(\frac{\alpha-\beta}{2}=32 \implies \alpha-\beta=64^{\circ}\).

By the inscribed angle theorem, \(\alpha=84^{\circ}\).

Thus, \(\beta=20^{\circ}\).

By the inscribed angle theorem, \(x=10^{\circ}\).

Answer:

Step-by-step explanation:

a)

Class limits       Frequency

38 - 63                  9

64 - 89                  7

90 - 115                 1

116 - 141                 1

142 - 167              2

Construct a histogram of these data(image attached)

b)

Frequency distribution table (also known as frequency table) consists of various components.

Classes: A large number of observations varying in a wide range are usually classified in several groups according to the size of their values. Each of these groups is defined by an interval called class interval. The class interval between 10 and 20 is defined as 10-20.

Class limits: The smallest and largest possible values in each class of a frequency distribution table are known as class limits. For the class 10-20, the class limits are 10 and 20. 10 is called the lower class limit and 20 is called the upper class limit.

Class limit: Class limit is the midmost value of the class interval. It is also known as the mid value.

Mid value of each class = (lower limit + Upper limit)2.  

If the class is 38 to 63 , lower limit is 38 and upper limit is 63. So the mid value is

\(\frac{(38+63)}{2} =50.5\)

Class width is calculated using upper and lower value

Class width = (upper - lower) value /class

\(=\frac{ ( 163 - 38)}{5} \\\\=25\)

Magnitude of a class interval: The difference between the upper and lower limit of a class is called the magnitude of a class interval.

Class frequency: The number of observation falling within a class interval is called class frequency of that class interval.

Answer:

direct proof, proof by contradiction, and proof by induction.

The number of people were 200 in the theater when it was full.

What is a theater?

In architecture, a theatre, usually spelled theatre, is a structure or area where a play can be conducted in front of spectators. The term comes from the Greek theatron, which means "a place of seeing." The actual performance usually takes place on a stage in a theatre.

Given that, the theater was full when the movie began.

76 people leave the theater before end the movie. At the end of the movie, there is 124 people left.

Apply algebraical operation that is addition to find the required answer.

Therefore, the number of people that was present at the beginning of the movie is (76 + 124) = 200.

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Answer:

it is because its being carried to the other side

Step-by-step explanation:

When you add 1 to negative 1 it becomes 0, so we are trying to make the right hand side equal to the left hand side. If that makes any sense.

Answer:

Step-by-step explanation: