find the quadratic function f(x)=ax2 bx c that goes through (4,0) and has a local maximum at (0,1).

The expression (5a)(3a + 2) simplifies to 15a^2 + 10a. This is obtained by multiplying 5a with both terms inside the parentheses using the distributive property. The final result cannot be further simplified. So, Option B is correct. Option B.

To simplify the given expression, (5a)(3a + 2), we apply the distributive property to distribute the factor 5a to both terms inside the parentheses. This involves multiplying 5a by each term separately.

First, we multiply 5a by 3a. Multiplying these two terms gives us 15a^2, where the coefficient 15 comes from multiplying 5 by 3 and the variable a is squared due to the multiplication of two a's.

Next, we multiply 5a by 2. This multiplication results in 10a, where the coefficient 10 comes from multiplying 5 by 2, and the variable a remains unchanged.

Combining the two simplified terms, we have 15a^2 + 10a. This expression cannot be further simplified because there are no like terms to combine.

The term 15a^2 represents the enlarged area of the mural, obtained by multiplying the lengths of the sides of the original square mural (side length a) by the factor 5 and squaring the variable a. The term 10a represents an additional area added during the enlargement process, obtained by multiplying the side length a by the factor 2.

In conclusion, the simplified form of (5a)(3a + 2) is 15a^2 + 10a. So OptioN B is correct.

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Answer:

14000Kilolitres

Step-by-step explanation:

\( 1megalitre = 1000kilolitres \\ \)

\(14megalitres = xkilolitres\)

Cross multiply

\(14 \times 1000 = xkilolitres\)

\(14megaitres = 14000kilolitres\)

Answer:

the number of cells increases by a factor of 2.

Explanation:

the number of cells doubles with each hour, which means that they are multiplied by 2. thus, the number of cells increases by a factor of 2.

i hope this helps! :D

Answer: The number of cells increases by a factor of 2.

After four hours, the number 2 is used as a factor 4 times.

Step-by-step explanation: The cells multiply by 2, and make double the amount of cells.

The number 2 is used 4 times after 4 hours to make 16 cells.

Answer:

Step-by-step explanation:

just plug in c

6-20 = 4 - 3(6)

When 293 college students are randomly selected and surveyed, it is found that 114 own a car. The upper limit for the 90% confidence interval for the percentage of all college students who own a car is 46.3%.

The given problem is an example of confidence intervals in statistics. The formula for finding the confidence interval in percentage is given below:

Confidence Interval in Percentage = P ± Z Score x √ (PQ/n)

where

P = Sample proportion

Q = 1 - P

n = Sample Size

Z Score is obtained from the Z-Table where the confidence level is given.

To obtain the upper limit, the following formula should be used:

Upper Limit of the Confidence Interval = P + Z Score x √ (PQ/n)

Substitute the given values of the question into the formula:

P = 114/293 = 0.3891

Q = 1 - 0.3891 = 0.6109

n = 293

The upper limit for the 90% confidence interval is given by the Z-Table at 1.645:

Upper Limit of the Confidence Interval = 0.3891 + 1.645 x √ [(0.3891 x 0.6109)/293]

≈ 0.3891 + 1.645 x 0.0467

≈ 0.3891 + 0.07701

≈ 0.4661 = 46.3%

Therefore, the answer is 46.3%.

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If x is the number 0.222…, then 10x = 2.222…. Subtracting x from 10x eliminates the fractional part, so that

10x - x = 2.222… - 0.222…

==>   9x = 2

and solving for x gives x = 2/9.

The answer of the given question based on probability is , option (A) 9/11.

Probability is  measure of  likelihood of  event occurring. It is number between 0 and 1, where 0 means that  event is impossible, and 1 means that  event is certain to occur. The probability of  event can be expressed as  fraction, a decimal, or a percentage. For example, if the probability of an event is 1/4, it means that there is a 25% chance of the event occurring.

The total number of hair clips in the box is:

Total number of hair clips = 15 (small) + 12 (medium) + 6 (large) = 33

The probability of selecting a small or medium hair clip is the sum of the probabilities of selecting a small hair clip and a medium hair clip:

P(small or medium) = P(small) + P(medium)

The probability of selecting a small hair clip is:

P(small) = number of small hair clips / total number of hair clips

= 15 / 33

The probability of selecting a medium hair clip is:

P(medium) = number of medium hair clips / total number of hair clips

= 12 / 33

Therefore, the probability of selecting a small or medium hair clip is:

P(small or medium) = P(small) + P(medium)

= 15/33 + 12/33

= 27/33

= 9/11

So the answer is (A) 9/11.

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There are 10560 ways we form a subcommittee of 5 members that have at least one member from each party.

Combinations are defined as the selections made by taking some or all of a number of objects, irrespective of their arrangements.

The number of combinations of n different things taken r at a time, denoted by nCr and it is given by,

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

where 0 ≤ r ≤ n.

The given information is committee has 8 republicans and 6 democrats.

we have to form a subcommittee of 5 members with at least one from each group.

Hence we need to select one from each and then the remaining 3 can be of any type.

No of ways =  ⁸C₁*⁶C₁*¹²C₃

                    = 48*220

No of ways=10560 ways.

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Answer:

1990 ml is the answer thank you

In order to prove the triangles are similar, you have to use SAS, SSS and AA rule.

In triangle, the similarity theorem states that if they have the same ratio of corresponding sides and equal pair of corresponding angles.

Here we have to find the 3 shortcuts to prove the triangles are similar.

According to the similarity theorem, here we have triangle that is similar to other if two pairs of angles are congruent (AA) or if two pairs of sides are proportional and the included angles are congruent whereas if three pairs of sides are proportional (SSS).

Here we must know that the term similarity and congruent are similar terms.

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Answer:

40%

Step-by-step explanation:

So add 18 and 12 makes 30. Then divide 30 with a common factor say 6. so there is 5 6s in 30 so each 6 is equivalent to 20 percent there are 2 6s in 12 so it is 40 percent

Answer: False!

This equation is in slope - intercept form, which is used to calculate and graph a line, and/or find the y - intercept and slope of a line. The standard form would be the equation before it was converted into slope - intercept form.

Hope this helps!

Answer:

False

Step-by-step explanation:

The y=mx+b form is called the slope-intercept form.

● m is the slope

● b is the y-intercept

● x is the variable (the input)

● y is the output

Answer:

the answer is 6 just check it

Answer:

The correct answer is: 2. t=0.45a

Step-by-step explanation:

Let t be the price of apples

and a be the number of apples

The price and quantity are directly proportional

\(t \propto a\)

Removing the proportionality symbol introduces a proportionality constant in the equation

\(t = ka\)

So far we know that cost of 6 apples is $2.70

Putting in the equation

\(2.70 = k (6)\\k = \frac{2.70}{6}\\k = 0.45\)

Putting the values of k will give us:

\(t = 0.45a\)

Hence,

The correct answer is: 2. t=0.45a

By definition of quotient, the rational number 1/3 represents a periodic infinite decimal number. That is to say, 1/3 is equivalent to the decimal number \(0.\overline{333}\)

The quotient of a fraction is found by dividing the fraction. Results in decimal form can be finite and infinite, infinite forms can be periodic or no periodic. This fraction represents a periodic infinite decimal number.

\(\frac{1}{3} = 0.\overline{333}\)

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The expression of the fraction 1/3 as a quotient is; 0 remainder 3 or 0 r 3.

Quotient is described as the quantity produced by the division of two numbers.

Now, we want to find the quotient of 1/3. It should be noted that this quotient should not be in decimal form and so it gives us;

0 remainder 3 since 3 as a denominator is bigger than 1 as numerator.

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Answer:

13 cm

Step-by-step explanation:

area = (1/2)(a + b)h

(1/2)(x + 9)(5) = 55

5x + 45 = 110

5x = 65

x = 13

The probability that a student selected at random will be a science or liberal arts major is 1/2 or 0.5.

First, let's find the total number of students in the class:
32 engineering majors + 24 science majors + 8 liberal arts majors = 64 students.
Next, let's find the number of science or liberal arts majors:
24 science majors + 8 liberal arts majors = 32 students.

Now, we can calculate the probability of selecting a science or liberal arts major at random.

The probability is given by the formula:
Probability = (Number of favorable outcomes) / (Total number of outcomes).
In this case, the favorable outcomes are selecting a science or liberal arts major, which is 32 students.

The total number of outcomes is the total number of students, which is 64.
So, the probability is:
Probability = 32/64.

To simplify the fraction, we can divide both the numerator and the denominator by their greatest common divisor (32):
Probability = 32/32 ÷ 32/32 = 1/2.

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The correct answer is option a. $7,594.46.

To calculate the amount you would reduce the amount you owe in the first year, we can use the formula for the equal installment of a loan. The formula is:

Installment = Principal / Number of Installments + (Principal - Total Repaid) * Interest Rate

In this case, the principal is $45,000, the number of installments is 5, and the interest rate is 8.5%.

Let's calculate the amount you would reduce the amount you owe in the first year:

Installment = $45,000 / 5 + ($45,000 - $0) * 0.085Installment = $9,000 + $3,825

Installment = $12,825

Therefore, you would reduce the amount you owe by $12,825 in the first year.The correct answer is option a. $7,594.46.

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The total number of boxes of inventory which is loading on the truck by the workers are 1,200 boxes.

What is percentage of a number?

Percentage of a number is the part of the number expressed in the in every hundred. Percentage of a number is expressed with the symbol '%'.

Workers are loading boxes onto a truck . So far, they have loaded 48 boxes onto the truck.

According to their inventory, they still need to load 96% of boxes on the truck. There must be 100% box at the start of the loading. Thus, the percentage of boxes they have load,

p=100-96 = 4%

Thus the percentage of boxes they have load in the truck is 4%. This is equal to the 48 boxes they have loaded.

Let suppose there is x number of total boxes. Thus the 4 percent of x will  be equal to the 48.

(4/100)x=48

x = 4800/4  = 1200

Thus, the total number of boxes of inventory which is loading on the truck by the workers are 1,200 boxes.

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Answer:

The slope of a linear model can be calculated using the formula:

m = Δy / Δx

where:

Δy = change in y (the dependent variable, in this case, total cost)

Δx = change in x (the independent variable, in this case, number of candy bars)

This is essentially the "rise over run" concept from geometry, applied to data points on a graph.

In this case, we can take two points from the table (for instance, the first and last) and calculate the slope.

Let's take the first point (3 candy bars, $6.65) and the last point (25 candy bars, $48.45).

Δy = $48.45 - $6.65 = $41.8

Δx = 25 - 3 = 22

So the slope m would be:

m = Δy / Δx = $41.8 / 22 = $1.9 per candy bar

This suggests that the cost of each candy bar is $1.9 according to this linear model.

Please note that this assumes the relationship between the number of candy bars and the total cost is perfectly linear, which might not be the case in reality.

Answer: where is statements

Step-by-step explanation:

Answer:B: m<3 = m<6

Step-by-step explanation: PLATO

Answer:

Answer:B: m<3 = m<6

Step-by-step explanation:

yess it is true because of unbiased estimator

what is variance?

Variability is measured by the variance. The average of the squared deviations from the mean is used to calculate it. The degree of spread in your data set is indicated by variance. The variance is greater in respect to the mean when the data are more dispersed

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Let's start graphing the first inequality y > 3x - 4. Since this is already in its slope-intercept form, we can see right away that the y-intercept of its boundary line is at (0, -4) and the slope is 3.

Aside from the y-intercept, let's find another point on the line using the slope. We will add 3 on the y-coordinate of the y-intercept and add 1 on the x-coordinate.

Hence, we have another point on the boundary line at (1, -1).

Let's plot these two points (0, -4) and (1, -1) and connect them using a dashed line since the inequality is "greater than". Also, the shade of the graph will be above the line.

The graph of the first inequality y > 3x - 4 is:

Moving on to the second inequality y ≤ x + 1, the y-intercept is at (0, 1) and the slope is 1.

Let's find another point on the line using the slope by adding 1 on the y-coordinate of the y-intercept and 1 on the x-coordinate.

Therefore, we have another point on the line at (1, 2).

Let's plot these points (0, 1) and (1, 2) on the graph. Connect them using a solid line because the inequality symbol has "or equal to". The shade of the graph will be below the line since the inequality symbol is "less than".

The graph of the second inequality y ≤ x + 1 is:

Combining the two graphs, we have:

The solution to the two inequalities would be the common shaded region, hence, in the diagram, it will be the darker shade.

Based on the given choices, this is shown by Option D.

Answer:

Jaylen was 16 years old. She's the oldest.

Step-by-step explanation:

16  Jaylen

15  sibling 1

14  sibling 2

13  sibling 3

12 sibling 4

11  sibling 5

10  sibling 6

____________

91  Total

My thinking was that I started out dividing 91 by 7. That came out 13. So I knew the oldest one had to be older than 13.

(a) If the current distribution is Ps all other Pa 0.2, then in the next period, all states will have the same probability of 0.2, because the frog has a 0.2 probability of moving to any state.

(b) If the current distribution is Pz 0.5, Ps 0.5 all other Pa 0.2, then in the next period, the probabilities of being in state z and state s will each be 0.5 * 0.5 = 0.25, and the probabilities of being in all other states will be 0.2.

(c) If the current distribution is Pz 0.225, Pa 0.25, Pa 0.5, all other P; 0.2, then in the next period, the probabilities of being in each state will be the sum of the products of the current probability of being in that state and the transition probabilities from that state.

(d) If the current distribution is P: Pz 0.22, Pa 0.22, Pa 0.22, Ps 0.22. P6 0.2, then in the next period, the probabilities of being in each state will be the same as in the current period, because the frog has an equal probability of moving to any state.

Note that in each case, the probabilities must add up to 1, as they represent the entire possible states of the frog.

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