Mathematics College

Help me with question 2, thank you!

Answers

Answer 1

Given the function f(x):

[tex]f(x)=3x^2-5x-4[/tex]

We will find the point on the given parabola where the slope of the tangent is horizontal

The horizontal line has a slope = zero

The slope of the line is the first derivative of the function

So, we will find the first derivative and equate it to zero

[tex]\begin{gathered} f^{\prime}(x)=0 \\ 3(2x)-5(1)-(0)=0 \end{gathered}[/tex]

solve the equation to find (x):

[tex]\begin{gathered} 6x-5=0 \\ 6x=5 \\ x=\frac{5}{6} \end{gathered}[/tex]

substitute with the value of (x) into the given function to find the y-coordinate

[tex]y=3(\frac{5}{6})^2-5(\frac{5}{6})-4=\frac{-73}{12}[/tex]

So, the answer will be the point will be as follows:

[tex](x,y)=(\frac{5}{6},\frac{-73}{12})[/tex]

See the following figure:

Related Questions

Pls help and thanks!

Answers

the multiplication of 2 matrices A and B

a11 a12 a13 ...

a21 a22 a23 ...

a31 a32 a33 ...

...

b11 b12 b13 ...

b21 b22 b23 ...

b31 b32 b33 ...

a11×b11+a12×b21+a13×b31+... a11×b12+a12×b22+a13×b32 ...

a21×b11+a22×b21+a23×b31+... a21×b12+a22×b22+a23×b32

a31×b11+a32×b21+a33×b31+... a31×b12+a32×b22+a33×b32

...

in other words, we combine the rows of the first matrix with the columns of the second matrix.

the rows of the result matrix are driven by the rows of the first matrix and the columns of the second matrix.

formally :

we can multiply a m×n matrix only with a n×o matrix.

the number of columns in the first matrix must be equal to the number of rows in the second matrix.

the result matrix is then sized m×o.

the first element (first row first column) of the result matrix is the sum of the products of the elements of the first row of the first matrix with the elements of the first column of the second matrix.

the element in the (x,y) position in the result matrix is the sum of the products of the elements of the xth row of the first matrix with the elements of the yth column of the second matrix.

so, when multiplying 2 2×2 matrices, the condition is automatically fulfilled : m = n = o = 2

ST =

4×0+1×-4 4×4+1×3

-3×0+-2×-4 -3×4+-2×3

-4 19

8 -18

and TS =

0×4+4×-3 0×1+4×-2

-4×4+3×-3 -4×1+3×-2

-12 -8

-25 -10

as we can see, the 2 results are completely different.

Classify each as corresponding, AIA, AEA, CIA,
or CEA
1)
3)
5)
X
y
2)
4)
++

Answers

Classify each as corresponding, AIA, AEA, CIA,
or CEA
1)
3)
5)
X
y
2)
4)
++

Selene's checking account balance was -$32, and then she withdrew $43 more. What is her checking account balance after the withdrawal?

Answers

Answer: $-75

Step-by-step explanation:

She took out money therefore the balance will go down. If we take 43 dollars from $-32 then we will get -75.

For scenarios of statistical studies are given below. Decide which study is a sample statistic

Answers

EXPLANATION

Since we have four given scenarios, the only viable option is the third one because It's the only statement where we take a sample (1000 individuals of 1883 participants).

Question four need to know what I did wrong I need to do it I need to understand

Answers

If there are 189 children, then there are 189 divided 7 = 27 groups of 7 children.

As mentioned in the problem, for every 7 children, there are 2 caretakers therefore, there are a total of 2 x 27 = 54 caretakers in the local daycare.

So, in total, there are 189 children + 54 caretakers = 243 people in the daycare facility.

01In Will's garden, 71 out of 200 plants have developed seends. Which is closest tothe percent of his plants that have developed seeds?

Answers

In this case, we'll have to carry out several steps to find the solution.

Step 01:

Data

plants have developed seeds = 71

total plants = 200

Step 02:

% = part / whole * 100

[tex]\text{percentage \% = }\frac{71}{200}\cdot100[/tex]

% = 35.5

The answer is:

35.5 %

5. Sales at Borders Books and Music stores increased from $2503 million in 1997 to $3699
million in 2003. Assuming that sales have been increasing exponentially, find an equation of
the form P = Poat, where P is Borders sales in millions of dollars and t is the number of years
since 1997. What is the percent growth rate?
B
Which of the following tables of values

Answers

In linear relationship, 199.333 million dollers per year is the percent growth rate.

What is linear relationship in math?

A statistical word used to express a straight-line relationship between two variables is a linear relationship (or linear association). Linear relationships can be represented graphically or mathematically as the equation y = mx + b.

Given , t Rs numbers of year since 1997 .

t = 0 corresponds to year 1997

t = 6 corresponds to year 2003

Let s(t) = sales of the year

So, given that

sales in 19997 is $2503 millions

so s(0) = 2503 million dollers

Sales in 2003 is $3699 millions

so s(6) = 3699 million dollers

Now apply formula of linear relation ship

s - s(0) = s(6) - s(0)/6 - 0 ( t - 0)

s - 2503 = 3699 - 2503/6 (t)

s = 1196* t /6 + 2503

so s(t) = 598t/3 + 2503

so now average rate of change of function over on interval is given by

= s(b) - s(a)/b - a

= s(6) - s( 0)/6 - 0

= 3699 - 2503/6

= 598/3

= 199.333 million dollers per year .

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Perform the following division: -48 / 5

A. 9.6
B. 8.1
C. -8.1
D. -9.6

Answers

The answer: -9.6
Hope this helps!

Name:
Math for College Liberal Arts
Classifying Data and Frequency Tables
Classify the following variables as qualitative (C) or quantitative (Q). (1 point each)
1. A list of telephone numbers:
3. Types of animals at a zoo :
11th graders
12th graders
Students at a local high school in grades 11 and 12 are asked what gaming system they
prefer. The results are summarized below in a two-way frequency table.
5. Complete the table. (6 points)
TOTAL
Nintendo Switch
132
11th graders
12th graders
TOTAL
Date:
?
?
2. Heights of players on a basketball team
4. Number of children in a family:
PS4
?
127
?
Neither
?
PS4
95
182
TOTAL
?
Use the table above to answer these questions. (1 point each)
6. How many 12th graders do not like either gaming system?
7. How many total students like the Nintendo Switch?
8. What is the total number of 11th grade students?
9. How many total students are there?
10. How many 11th graders like the PS4?_
11. Create a relative frequency table from the table above. Write the relative frequencies as decimals
rounded to two decimal places. (12 points)
Nintendo Switch
Neither
315
655
TOTAL

Answers

Numerical variables are the subject of quantitative data. Qualitative data can be represented by a name, symbol, or number code and are measures of "types."

What are qualitative variables and quantitative variables?

Numerical variables are the subject of quantitative data. Qualitative data can be represented by a name, symbol, or number code and are measures of "types." Data concerning categorical variables make up qualitative data.

Quantitative Variables with values obtained through measurement or counting. Variables that exists not measurement variables are referred to as qualitative variables. Their values are not determined by counting or measuring. Values that are used to identify people in a table are called designators. While qualitative research focuses on words and meanings, quantitative research deals with figures and statistics.

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Find the common difference and the next two terms of the arithmetic sequence.11,19,27,35The common difference isWrite the next two terms in the sequence:11,19,27,35,?,?

Answers

The common difference in the given arithmetic sequence is 8.

What is an arithmetic sequence?An ordered group of numbers with a shared difference between each succeeding term is known as an arithmetic sequence. For instance, the common difference in the arithmetic series 3, 9, 15, 21, and 27 is 6. The arithmetic mean can be calculated as one approach. Divide the total by the total number of values after adding up all the values. Add the numbers together, for instance: a + b + c + d and so on, if there is a set of "n" numbers.

So, formula for common differences:

d = (aₙ₊₁ - aₙ)

Now, insert terms in the formula as follows:

d = (aₙ₊₁ - aₙ)d = (19 - 11)d = 8

Therefore, the common difference in the given arithmetic sequence is 8.

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Find the slope of the line graphed below.

Answers

Answer:

[tex]\frac{-5}{2}[/tex]

Step-by-step explanation:

There are two blue dots on the graph. It does not matter which dot you startr at. Let's start at the bottom, right dot. How many space up and to the left you do you have to move to get to the second dot?

You need to move 5 dots straight up. Up is a positive direction. Then you have to move 2 spaces left. Left is a negative direction, so your slope will be negative.

- [tex]\frac{5}{2}[/tex] [tex]\frac{-5}{2}[/tex] [tex]\frac{5}{-2}[/tex] All of these mean the same thing.

At age 19, someone sets up an IRA (individual retirement account) with an APR of7 %. At the end of each month he deposits $20.00 in the account. How much will the IRA contain when he retires at age 65? Compare that amount to the total deposits made over the time period.

Answers

The amount of IRA when he will retire at age 65 = $83448.27

And the total deposits made over the time period is less than the the amount of IRA

We have been given, at age 19, someone sets up an IRA (individual retirement account) with an APR of7 %. At the end of each month he deposits $20.00 in the account.

We need to find the IRA when he retires at age 65.

here, 65 - 19 = 46 years

So, the period would be,

46 × 12 = 552 months

Monthly deposit= $20

And the interest rate would be,

Interest = 0.07/12

= 0.0058

To calculate the future value, we need to use the following formula:

FV= {A × [(1 + i)^n-1]} / i

A= monthly deposit

i = interest rate

n = period

So, the Future Value of Annuity

= 20 × ([1 + 0.0058]^552 - 1 ) / (0.0058)

= 20 × 24.2 / 0.0058

= $83448.27

So, the amount of IRA when he will retire = $83448.27

Deposits made over the time period = 20 × 46 × 12 = $‭11040

Difference = 83448.27 - 11040

= $72408.27

This means, the total deposits made over the time period is less than the the amount of IRA he will get when he retires at age 65.

Therefore, the amount of IRA when he will retire at age 65 = $83448.27

And the total deposits made over the time period is less than the the amount of IRA

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Simplify this expression 2 x x 3 x y

Answers

Answer:

6[tex]x^{2}[/tex]y

Step-by-step explanation:

If I ready your explanation correctly it is

2x3xy We multiply the 2 and 3 and the xx would be [tex]x^{2}[/tex]

When making homemade ice cream in a hand-cranked freezer, the tub containing the ice cream mix is surrounded by a brine (water/salt) solution. To freeze the ice cream mix rapidly so that smooth and creamy ice cream results, the brine solution should combine crushed ice and rock salt in a ratio of 5 to 1. A small ice cream freezer requires 10 cups of crushed ice. How much rock salt should be mixed with the ice to create the necessary brine solution?

Answers

Answer:

Beginning with 23 grams of a radioactive element whose half-life is 45 years, the mass y (in grams) remaining after t years is given byy = 23(1/2)^t/45, t ≥ 0.How much of the initial mass remains after 170 years? (Round your answer to three decimal places.)

Answers

[tex]y\approx1.677g[/tex]

1) As we were told of the half-life formula along with the data, we can write out the following to get the remains after 170 years:

[tex]\begin{gathered} y=23(\frac{1}{2})^{\frac{t}{45}} \\ y=23(\frac{1}{2})^{\frac{170}{45}} \\ y=23(\frac{1}{2})^{\frac{170}{45}}^ \\ y\approx1.677 \end{gathered}[/tex]

2) So, according to this model we can tell there will be left approximately

[tex]1.677g[/tex]

3 is grater than or equal to W and -5 is less than W write as an inequality

Answers

Answer: 3 ≥ W > -5

Step-by-step explanation:

Just look at the way the question is asked, that is the best I can explain. Sorry.

4 ≤-3x - 1≤9
What is the compound inequality

Answers

Answer:

−1≤x<3

Step-by-step explanation:

−4≤3x−1<8

−4≤3x−1and3x−1<8

3x−1≥−4and3x−1+1<8+1

3x≥−3and3x<9

x≥−1andx<3

−1≤x<3

Give a counterexample to the following conditional statement. Write your answer as a number. If |x+ 4|= 8, then x=−12

Answers

he Solution:

iven in the question that if

[tex]|x+4|=8\text{ then x=-12}[/tex]

We are required to give a counterexample to the given conditional statement above.

[tex]\begin{gathered} |x+4|=8 \\ \text{Means that} \\ x+4=8\text{ or x+4=-8} \end{gathered}[/tex]

Solving each of the equations above, we get

[tex]\begin{gathered} x+4=-8 \\ x=-8-4 \\ x=-12 \\ Or \\ x+4=8 \\ x=8-4 \\ x=4 \\ \text{ So, } \\ x=-12\text{ or x=4} \end{gathered}[/tex]

So, the counterexample to the given conditional statement is x = 4.

Part 1 of 2
Your friend says that the solutions to the inequality 6x-19x≤52 are xs-4. Solve the inequality correctly. What error did your friend
make?

Answers

Answer is 54 got the test back

When x =1/2 and y = 1/8, -5x + 14y =

Answers

Answer:

-5x1/2= -2.5 14x1/8= 1.75

Step-by-step explanation:

-2.5+1.75=-0.75

Answer:

-3/4

Step-by-step explanation:

Plug in values of x and y into expression:

[tex]-5(\frac{1}{2})+14(\frac{1}{8})=[/tex]

[tex]-\frac{5}{2} +\frac{14}{8}=[/tex]

Find common denominator:

[tex]-\frac{5*4}{2*4} +\frac{14}{8}=[/tex]

[tex]-\frac{20}{8} +\frac{14}{8}=\frac{14}{8}-\frac{20}{8}=[/tex]

Solve numerator:

[tex]14-20=-6[/tex]

So,

[tex]=-\frac{6}{8}=-\frac{3}{4}[/tex]

How many solutions does the equation. a| x + b | + c = d have when a > 0 and c = d? When a < 0 and c > d ? Explain your reasoning.

Answers

In the first case the equation has only one unique solution and in the second case the equation has many solutions.

We are given the equation a|x + b| + c = d and we need to determine the solution of this equation when a > 0 and c = d. The equation contains absolute value symbol which always gives a positive value. The equation can be written as

a|x + b| + c = d

a|x + b| = d - c, since c = d then we can write equation as

a|x + b| = 0, Now, a > 0

=> |x + b| = 0

=> x = -b that is only one unique solution.

Now, in second case a < 0 and c > d then

a|x + b| = d - c

If c > d, then the left-hand side of the equation becomes negative and also a < 0 so the right-hand side also becomes negative. So, the equation will have many solutions in this case.

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Solve each system by graphing, and then write the solution. x + 4 = - y-6y + 9x = - 6

Answers

To solve the given system of equation by graphing you only have to graph both lines. The solution is the intersection between the lines.

According to this, the intersection of the two lines is (-2, -2). It means that the solution is (-2, -2).

The bill for dinner was $61.66. You left $10.34 for the tip. What percentage of the original bill was the tip? Round your a
to the nearest whole percent.

Answers

Answer:

17%

Step-by-step explanation:

You want the percentage represented by a tip of $10.34 on a dinner bill of $61.66.

Percentage

A percentage is a fraction that has been multiplied by 100%:

10.34/61.66 × 100%

≈ 0.168 × 100%

≈ 17%

The tip was about 17% of the original bill.

The number must be a one digit number, When the number is added to 746 the digit in the ones place of the sum is less than the ones digit in 746.

Answers

The one digit numbers that when added to 746 gives a digit in the ones place of the sum which is less than the ones digit in 746 are;

4, 5, 6, 7, 8, or 9

What is a place value?

Place values is the value a digit in a number posseses based on its position in the number

The given parameters of the number are;

The number of digits in the number = 1

The ones digit of the sum of the number and 746 is less than the ones digit in 746, which is 6

Therefore;

The value of the number when added to 746 can be expressed as 7xy

Where;

y < 6

The process of adding two numbers involves the addition of the numbers based on their place values such that the ones digit part of the result is placed as the output while the 1 in a result that is 10 or more is added to the next higher place value number to the left of the added digits

Therefore, to have a value of the digit in the ones place less than 6, we can have;

746 + 0 = 746

746 + 1 = 747

746 + 2 = 748

746 + 3 = 749

746 + 4 = 750; 0 < 6746 + 5 = 751; 1 < 6746 + 6 = 752; 2 < 6746 + 7 = 753; 3 < 6746 + 8 = 754; 4 < 6746 + 9 = 755; 5 < 6

The possible one digit numbers that gives a sum with a ones digit less than 6 when added to 746 therefore includes; 4, 5, 6, 7, 8, and 9

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4. The ages of the members of a volunteer group are shown below: 13, 14, 14, 14, 15, 15, 15, 16, 16, 21, 23 Which box plot best represents this data? F 13 15 17 19 21 23 13 15 17 21 23 H < 15 19 15 17 19 21

Answers

First, we need to calculate the median

13, 14, 14, 14, 15, 15, 15, 16, 16, 21, 23

we have 11 values the media is the 6th value in this case 15.

the lower extreme is 13 the upper extreme is 23.

The lower quartile is 14 and upper quartile is 16

the box plot is

If f (x) = -3x - 2, find the value
ƒ(-7)

Answers

Answer:

Step-by-step explanation:

-3(-7)-2

21-2

it need to be at least 20 chqracters so ignore this the answer is at the top

-7×+8=-4x = ? trying to understand this

Answers

[tex]x\text{ = }\frac{12}{7}[/tex]

Here, we want to get the value of x

We can get this by isolating x

We start by bringing like terms together

[tex]\begin{gathered} -7x\text{ = -4-8} \\ \\ -7x\text{ = -12} \\ \\ x\text{ = }\frac{-12}{-7} \\ \\ x\text{ = }\frac{12}{7} \end{gathered}[/tex]

It is a decimalllllllllllllllllllll

A flower bed is in the shape of a triangle with one side twice the length of the shortest side, and the third side is 22 feet more than the length of the shortest side. Find the dimensions if the perimeter is 186 feet.

Answers

The three sides of the triangle will be 82, 63, and 41 feet.

What is a triangle?

Triangle is a shape made of three sides in a two-dimensional plane. the sum of the three angles is 180 degrees. The perimeter of the triangle is the sum of all three sides of the triangle.

That a flower bed is in the shape of a triangle with one side twice the length of the shortest side, and the third side 22 feet more than the length of the shortest side.

Let the three sides of the triangle be A, B, and C. Here A is the longest side B is the shortest side and C is the third side.

Perimeter = A + B + C

A = 2B and C = 22 + B

Put the values in the equation as solve:-

Perimeter = A + B + C

186 = 2B + B + 22 + B

186 = 4B + 22

4B = 186 - 22

4B = 164

B = 164 / 4

B = 41 feet

Longest side = 2B = 2 x 41 = 82 feet

Shirtest side = B = 41 feet

Third side = 22 + B = 22 + 41 = 63 feet

Therefore, the three sides of the triangle will be 82, 63, and 41 feet.

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What is the probability of having exactly 2 boys in 3 births AND having exactly 2 girls in 3 births? (Equal chance of any)

Answers

the probability of having exactly 2 boys in 3 births AND having exactly 2 girls in 3 births is 3/8.

What is the difference between permutation and combination in probability?For a list of data, where the order of the data is important, a permutation is used, while for a group of data, where the order of the data is irrelevant, a combination is used.Combinations exist when the order doesn't matter, but permutations exist when it does. A permutation could be described as an ordered combination. The following formula determines how many permutations of n objects, taken r at a time: P(n,r)=n!

the possible outcomes are

BBB,BBG,BGB,GBB,BGG,GBG,GGB,GGG

wherein 3 meet the requirement. There are 8 possible outcomes, all equally likely (if we assume each gender is equally likely). Hence the choice is 3/8.

We can also think about it in at least one more way: You identified all the possible ways to get 2 boys and one girl. Since the events are disjoint, we can add up the probabilities

P(2 boys, 1 girl)=P(BBG)+P(BGB)+P(GBB)

=[tex]\frac{1}{2} X\frac{1}{2} X \frac{1}{2}[/tex]+ [tex]\frac{1}{2} X\frac{1}{2} X \frac{1}{2}[/tex] + [tex]\frac{1}{2} X\frac{1}{2} X \frac{1}{2}[/tex]

= 3/8.

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A dealer sold a watch 130% of his cost. If the sale price was $39, how much did the cost the dealer? Please show your work.

Answers

The cost of the watch which sold at 130% of its cost and sale price is $39 is equal to $30.

As given in the question,

Sale price of the watch for which dealer sold = $39

Let $'x' be the cost of the watch with which dealer purchase

A dealer sold a watch 130% of its cost

Required expression to show the given condition of a dealer is given by:

130% of x = $39

⇒ (130 /100) × x = $39

⇒ x = ( 39 × 100 ) / 130

⇒ x = $30

Therefore, the cost of the watch which sold at 130% of its cost and sale price is $39 is equal to $30.

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