Answers
The values for the determinants of the matrices are:
|A| = -3
|B| = -2
|AB|= -6
How to determine the determinant of A, |A|?A matrix (plural matrices) is a set of numbers arranged in rows and columns so as to form a rectangular array.
If the matrix Z is given as:
[tex]Z = \left[\begin{array}{ccc}a&b\\c&d\end{array}\right][/tex]
The determinant will be:
|Z| = (a * d) - (b * c)
Thus:
|A| = (-1 * 3) - (0 * 0) = -3
|B| = (2 * (-1)) - (0 * 0) = -2
AB = A * B
[tex]AB = \left[\begin{array}{ccc}-1&0\\0&3\end{array}\right] * \left[\begin{array}{ccc}-2&0\\0&-1\end{array}\right][/tex]
Calculations for the product (multiply each row by each column):
[-1 * (-2)] + [0 * 0] = 2
[-1 * 0] + [0 * (-1)] = 0
[0 * (-2)] + [3 * 0] = 0
[0 * 0] + [3 * (-1)] = -3
[tex]AB = \left[\begin{array}{ccc}2&0\\0&-3\end{array}\right][/tex]
Thus,
|AB| = (2 * (-3)) - (0 * 0) = -6
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Related Questions
The graph of a sine function has an amplitude of 4, a midline of y=2, and a period of 10.
There is no phase shift. The graph is reflected over the x-axis.
What is the equation of this function?
Answers
The equation of the given sine function is y = 4 × sin((π/5)x) + 2.
The equation of the given sine function can be determined based on the given information. We know that the general form of a sine function is:
y = A × sin(Bx - C) + D,
where A represents the amplitude, B represents the frequency, C represents the phase shift, and D represents the vertical shift.
In this case, we are given the following information:
Amplitude (A) = 4: The amplitude is the distance between the maximum and minimum values of the function. Since the function is reflected over the x-axis, the amplitude is positive 4.
Midline (D) = 2: The midline is the horizontal line around which the graph oscillates. In this case, it is y = 2, indicating a vertical shift of 2 units upwards.
Period = 10: The period is the distance between two consecutive peaks (or troughs) of the function.
Given that there is no phase shift, the phase shift (C) is 0.
From the given information, we can deduce the values of A, B, C, and D to construct the equation.
A = 4 (amplitude)
D = 2 (vertical shift)
C = 0 (no phase shift)
To determine B, we use the formula:
B = 2π / Period
Plugging in the value for Period (10), we can calculate B:
B = 2π / 10 = π / 5
Therefore, the equation of the given sine function is:
y = 4 × sin((π/5)x) + 2.
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imagine that a friend asks you for investment advice. he bas $10,000 to invest and he has about 35 years before he will be ready for his financial goal of early retirement. what types of investments would you recommend to your friend? why? what other investing advice would you give him to help him achieve his financial goals?
Answers
When it comes to long-term investment goals like early retirement, it is generally recommended to focus on investments that offer potential growth over an extended period of time. Here are some investment options and advice that could be beneficial for your friend:
Stock market investments: Investing in a diversified portfolio of stocks can provide the potential for long-term growth. Your friend can consider investing in individual stocks or exchange-traded funds (ETFs) that represent a basket of stocks.
Mutual funds: Mutual funds offer diversification by pooling money from multiple investors to invest in a variety of assets. They are managed by professionals who make investment decisions on behalf of the investors.
Index funds: Index funds are a type of mutual fund that aims to replicate the performance of a specific market index, such as the S&P 500. They offer broad market exposure and generally have lower expense ratios compared to actively managed funds.
Retirement accounts: Encourage your friend to take advantage of tax-advantaged retirement accounts like a 401(k) or an individual retirement account (IRA). These accounts provide tax benefits and can help grow savings faster.
Dollar-cost averaging: Advising your friend to invest regularly, regardless of market conditions, through a strategy called dollar-cost averaging can help mitigate the impact of market volatility. By investing a fixed amount at regular intervals, your friend will buy more shares when prices are low and fewer shares when prices are high.
Rebalancing: As time goes on, it's important to periodically review and rebalance the investment portfolio. This involves adjusting the asset allocation to maintain the desired level of risk and return. Regularly rebalancing ensures that the investments stay aligned with the financial goals and risk tolerance.
Emergency fund: Remind your friend about the importance of building an emergency fund with three to six months' worth of living expenses. This will provide a safety net and help prevent the need to tap into long-term investments during unforeseen circumstances.
Seek professional advice: Depending on your friend's knowledge and comfort level with investing, it may be helpful to recommend consulting with a financial advisor who can provide personalized advice based on their specific financial situation and goals.
Remember, investing involves risks, and it's crucial for your friend to carefully evaluate investment options, consider their risk tolerance, and have a long-term perspective. Regularly monitoring and adjusting the investment strategy over time will help ensure progress towards achieving their financial goals.
Find the volume of the pyramid above
Find the surface are of the pyramid above pls help
Answers
The volume of the pyramid is 18069333.33 units³ and the surface area is 391600 units ²
What is a pyramid?A pyramid is a three-dimensional figure. It has a flat polygon base. All the other faces are triangles and are called lateral faces.
Surface area of a pyramid is expressed as;
area of 4 lateral face + area of base
area of base = 440²
= 193600 units²
area of a lateral = 1/2 bh
= 1/2 × 440 × 356
= 78320
For four surfaces = 4 × 78320 = 313280
Total surface area = 313280+78320
= 391600 units ²
Volume of a pyramid is expressed as;
V = 1/3base area × height
V = 1/3 × 440² × 280
V = 18069333.33 units³
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select all answers that are similar to polygon K
Answers
Answer:
B, C, D
Step-by-step explanation:
You want to identify the shapes that are similar to polygon K.
Right trianglePolygon K is a right triangle that has leg lengths in the ratio 4:2 = 2:1.
Polygons B, C, and D are right triangles similar to polygon K:
B is a dilation by a factor of 1/2C is a reflection of BD is a rotation of KOthersPolygons A and E are also right triangles, but have different ratios of leg lengths. In A they are 1/1, and in E they are 4/3. These triangles are not similar to triangle K.
__
Additional comment
Polygons similar to the same polygon are similar to each other. Rigid transformations such as reflection and rotation result in figures congruent to the original. Congruent figures are also similar.
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Write the following number in expanded form: fifty-four and eight tenths
Answers
Fifty-four and eight tenths" can be expressed in expanded form as the sum of 54 (representing 50 + 4) and 0.8, which represents the decimal part.
To write the number "fifty-four and eight tenths" in expanded form, we can break it down into its individual place values and numerical components.
The number "fifty-four" can be broken down as follows:
The digit 5 represents the value of 50, which is 5 tens.
The digit 4 represents the value of 4, which is 4 ones.
So, "fifty-four" can be expressed as 50 + 4.
Next, we have "eight tenths". This can be expressed as 8/10 or simply 0.8 since each tenth is equal to 0.1.
Putting it all together, the number "fifty-four and eight tenths" can be written in expanded form as:
50 + 4 + 0.8
Simplifying further, we can combine the integer and decimal parts:
54 + 0.8
Therefore, the expanded form of "fifty-four and eight tenths" is 54 + 0.8.
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6. The circle graph gives the percentage
of students who favor the different lunch
menus offered by the school cafeteria.
Find mKL and mLMJ. (6 POINTS)
J
Chicken Fingers
Corn Dogs
31%
30%
M
C
K
Spaghetti
15%
Pizza
24%
L
Answers
The circle graph percentage is solved and the measure of ∠KL = 54° and the measure of ∠LMJ = 198°
Given data ,
Let the circle graph gives the percentage of students who favor the different lunch menus offered by the school cafeteria
Now , the measures of the angles are given by
The measure of ∠KL = 15 %
15 % ( 360 ) = 54°
Therefore , the measure of ∠KL = 54°
And , the measure of ∠LMJ = ( 24 % + 21 % ) of 360
The measure of ∠LMJ = 198°
Hence , the circle graph percentage is solved
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Use the diagram to find x and y
Answers
The values of x and y is x=8 and y=12.
We are given that;
The dimensions=7 and 24
Now,
(x+y)^2= 7^2 + 24^2
x^2+y^2+2ab=49+416
x^2+y^2+2xy=465
Also, 7^2=x2+h2
49=x2+15
x2=49+15
x2=64
x=8
Substituting the values of x
8+y=20
y=12
Therefore, by Pythagoras theorem the answer will be x=8 and y=12.
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Carter is going to invest in an account paying an interest rate of 4.3% compounded daily. How much would Carter need to invest, to the nearest ten dollars, for the value of the account to reach $174,000 in 19 years?
Answers
Carter would need to invest approximately $76,869.06 to reach a value of $174,000 in 19 years with a 4.3% annual interest rate compounded daily.
What is the principal that needs to be invested?The formula accrued amount in a compounded interest is expressed as;
[tex]A = P( 1 + \frac{r}{n})^{(nt)}[/tex]
Where A is accrued amount, P is principal, r is interest rate and t is time.
Given that:
Accrued amount A = $174,000
Compounded daily n = 365
Time t = 19 years
Interest rate r = 4.3%
Principal P = ?
First, convert R as a percent to r as a decimal
r = R/100
r = 4.3/100
r = 0.043
Plug these values into the above formula and solve for principal P.
[tex]A = P( 1 + \frac{r}{n})^{(nt)}\\\\A = 174,000( 1 + \frac{0.043}{365})^{(365\ *\ 19)}\\\\A = \$ 76,869.06[/tex]
Therefore, the principal that needs to invested is $76,869.06.
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PLS HELP! What is the domain and Rage of the given below?
And is it a Function or not?
X /-2/-2 /-1 /-1 /0
Y/ 5/-5/ 3/-3/-1
Answers
In Functions and Function Notation, we were introduced to the concepts of domain and range. In this section we will practice determining domains and ranges for specific functions. Keep in mind that, in determining domains and ranges, we need to consider what is physically possible or meaningful in real-world examples, such as tickets sales and year in the horror movie example above. We also need to consider what is mathematically permitted. For example, we cannot include any input value that leads us to take an even root of a negative number if the domain and range consist of real numbers. Or in a function expressed as a formula, we cannot include any input value in the domain that would lead us to divide by 0.
Diagram of how a function relates two relations.
We can visualize the domain as a “holding area” that contains “raw materials” for a “function machine” and the range as another “holding area” for the machine’s products.
We can write the domain and range in interval notation, which uses values within brackets to describe a set of numbers. In interval notation, we use a square bracket [ when the set includes the endpoint and a parenthesis ( to indicate that the endpoint is either not included or the interval is unbounded. For example, if a person has $100 to spend, he or she would need to express the interval that is more than 0 and less than or equal to 100 and write
(
0
,
100
]
. We will discuss interval notation in greater detail later.
Let’s turn our attention to finding the domain of a function whose equation is provided. Oftentimes, finding the domain of such functions involves remembering three different forms. First, if the function has no denominator or an even root, consider whether the domain could be all real numbers. Second, if there is a denominator in the function’s equation, exclude values in the domain that force the denominator to be zero. Third, if there is an even root, consider excluding values that would make the radicand negative.
Before we begin, let us review the conventions of interval notation:
The smallest term from the interval is written first.
The largest term in the interval is written second, following a comma.
Parentheses, ( or ), are used to signify that an endpoint is not included, called exclusive.
Brackets, [ or ], are used to indicate that an endpoint is included, called inclusive.
At the farmers' market, Tom bought 11/12 of a pound of string beans and 1/2 of a pound of
lima beans. How many more pounds of string beans did Tom purchase?
Write your answer as a fraction or as a whole or mixed number.
pounds
Answers
Answer:
Step-by-step explanation:
5/12 pounds more
Side panel MF Open course index Open block drawer Learnership Pre-Assessment and Evaluation v1 Figure Classification Assessment  QUIZ Figure Classification Assessment Back Time left 0:59:33 Question 1 Not yet answered Not graded Flag question Question text This test consists of several different items. Each item of the test appears in a separate question. The form of an item - item 25, say, is as follows:  You will notice that there are six boxes: 1 box in the first row 2 boxes in the second row, and 3 boxes in the third row In the top left-hand corner of each box, there is a letter labelling each box. For example, the letter ‚"A" labels the box in the first row. The number, which appears to the left of the box ‚"A" is the number of the item. In this example, it is item 25. Every item of the test will have this form, with each box containing a drawing of shapes or patterns. The following is an example of an item:  You must group the 6 drawings into two groups of 3 drawings each. The drawings of each group must be similar to one another in some way - they must belong together. In the example - item 25 - drawings A, B and F belong together because they are shaded the same way, and drawing C, D and E belong together because their shadings are the same. Now turn to your answer sheet and look at it carefully. At the top of the page is 2 rows of 6 boxes. The first row of the boxes refers to the item "Example (i)" and the second row of the boxes refer to the item "Example (ii)." Below these two rows are 24 rows of 6 boxes. Each row refers to a particular item of the test. The number which appears to the left of each row of boxes refers to the item number in the test. Each row of 6 boxes is divided into 2 groups of 3 boxes. The first box of each row contains the letter "A". In the following two empty boxes, you insert the letters of the two drawings which belongs to the same group as that to which drawing A belongs. In the second group of 3 empty boxes you must insert the letters of the other 3 drawings which belong together. Here is another example of an item - item 26.  In this item, drawings A, D and E belong together because their outlines consist of single lines. Drawings B, C and F belong together because their outlines consist of double lines. The answer to this practice item should be filled in as follows:  Please note the following: 1. It is NOT correct to find a reason for grouping together 3 drawings of an item, and assume that the other 3 drawings belong together. For example, when solving item 26 (Previous page), it would be incorrect to group together drawings A, E and F on the basis that each of these is a 4-sided figure, and drawings B, C and D on the basis that they do not have 4 sides. You must be able to find something common to the 3 drawings of each group. 2. A drawing may NOT belong to both groups. For example, the response-  would be incorrect since the drawing "D" is common to both groups. Select one: a. Continue b. Ask for assistance Clear my choice Question 2 Not yet answered Not graded Flag question Question text You must now do two example items on your own. These examples are on the next two pages. Please fill in the answers to the two examples in the first two rows of the answer sheet. These two rows are labelled “Example (i)" and “Example (ii)". Group the 6 drawings into two groups of 3 drawings each. The drawings of each group must be similar to one another in some way - they must belong together. Hint: Type the answer as one word e.g. ABC  Answeris the first group. Answeris the second group.
Answers
The solution is: the dimensions of the flag in inches is:
40 inches by 55 inches.
The flag is rectangular in nature and the formula for calculating the perimeter of a rectangle is P = 2(L+W) where;
L is the length of the flag
W is the width of the flag
From the diagram, L = y and W = 11y/8
Since the perimeter = 190 inches, we will substitute the given parameters into the formula and firs calculate the value of y.
190 = 2(y+11y/8)
190 = 2y + 11y/4
multiply through by 4
760 = 8y+11y
760 = 19y
y = 760/19
y = 40
The length of the flag is 40 inches and the Width of the flag is 11(40)/8 = 55inches.
Hence, the dimensions of the flag in inches is 40 inches by 55 inches.
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complete question:
Item 15 Question 1 Write and solve an equation to answer the question. The perimeter of the Norwegian flag is 190 inches. What are the dimensions of the flag? Equation: =190 y= Question 2 Label the dimensions of the flag in inches.
Answer:
Step-by-step explanation:
Which of the following is not the solution of system of inqualities
(1,0) (8,0). (0,4). (3,0)
Answers
The points (1,0) (8,0). and. (3,0) are not the solution of system of inqualities
How to deterine which is not the solution of system of inqualitiesFrom the question, we have the following parameters that can be used in our computation:
The graph
Also, we have the following ordered pairs
(1,0) (8,0). (0,4). (3,0)
From the graph, we have the following ordered pairs in the shaded region
(0, 4)
Other points (1,0) (8,0). and. (3,0) are not in the shaded region
This means that (1,0) (8,0). and. (3,0) are not the solution of system of inqualities
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Over the past few years Donald made 4 trips to the amusement park he drove 399KM in all the distance traveled by him on each trip to the park is
Answers
Donald traveled approximately 100 kilometers on each of his trips to the amusement park.
Now, the distance Donald traveled on each of his trips to the amusement park.
If he drove a total of 399 kilometers over the course of four trips, we can find the average distance he traveled per trip by dividing the total distance by the number of trips.
So, We get;
= 399 divided by 4
= 399 / 4
= 99.75 kilometers per trip
≈ 100 kilometers per trip.
Therefore, Donald traveled approximately 100 kilometers on each of his trips to the amusement park.
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Identify the part, percent and base.
$37.60 interest earned on a $460 investment at 8%.
Part:
Percent:
Base:
Answers
The given information is,$37.60 interest earned on a $460 investment at 8%.
Part:The amount of interest earned is called the part. Here, the amount of interest earned is $37.60. Hence the part is $37.60.
Percent:The rate per 100 units of the base is called the percent. Here, the percent rate is 8%.
Base:The original amount invested or borrowed is called the base. Here, the original investment amount is $460. Hence the base is $460.
Thus,
Part: $37.60
Percent: 8%
Base: $460.
Part: The part is the interest earned, which is $37.60.
Percent: The percent is 8%, which represents the annual interest rate.
Base: The base is the amount of the investment, which is $460.
four students are trying to find the rule that translates point N(-2,-4) to N'(2,4)
Answers
The student that gets the rule of the transformation correctly is Raheem
How to determine the student that gets the rule correctlyFrom the question, we have the following parameters that can be used in our computation:
Point N = (-2, -4)
Image of the point N = (2, 4)
This means that
N = (-2, -4)
N' = (2, 4)
From the above, we can see that
N' = -1 * N
This means that
N' = (-2, -4) * -1
So, we have
N' = (-2* -1 , -4 * -1)
So, the rule is (x * -1, y * 1)
Hence, the student that gets the rule correctly is Raheem
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Question
Four students are trying to find the rule that translates point N(-2,-4) to N'(2,4). Each student’s reasoning is shown below.
Raheem: The rule is (x * -1, y * -1)
Casey: The rule is (x + 2, y + 4)
Andrew: The rule is (x + 4, y + 0)
Lo: The rule is (x + 4, y + 8)
Which student is correct?
Raheem
Casey
Andrew
Use the Law of Cosines to solve the problem. You must solve for BC first. Solve this problem in order.
A ship travels due west for 94 miles. It then travels in a northwest direction for 119 miles and ends up 173 miles from its original position. To the nearest tenth of a degree, how many degrees north of west (x) did it turn when it changed direction? Show your work.
Answers
In a case whereby A ship travels due west for 94 miles. It then travels in a northwest direction for 119 miles and ends up 173 miles from its original position the degrees north of west it turned is 72°
How can the degree be calculated?From trigonometry, the law of cosines states the side c of a triangle can be found as
c² = a² + b² - 2abcos(C)
where
C = angle opposite to side c.
a and = lengths of the other sides.
a = 94, b = 119, c = 173.
c² = a² + b² - 2abcos(C)
173² = 94² + 119² - 2 x 94 x 119cos(C)
22327cos(C) = -6932
cos(C) = -6932/22327
C = arccos(-6932/22327)
C = 108º.
Then,
T = 180 - C
= 180 - 108 = 72º.
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Given y=4x+2, find the domain value if the range value is 4
Answers
4-2=4x+2-2
2=4x
Divided both sides by 4
X=1\2
The domain value that corresponds to a range value of 4 is,
⇒ x = 1/2
Given that;
Function is,
y = 4x + 2
Since, the equation equal to the range value:
4 = 4x + 2
Then, we can solve for "x":
4 - 2 = 4x
2 = 4x
x = 1/2
Now that we have the value of "x", we can find the corresponding value of "y" by substituting it into the given equation:
y = 4x + 2
y = 4(1/2) + 2
y = 4 + 2
y = 6
Therefore, the domain value that corresponds to a range value of 4 is,
⇒ x = 1/2
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Need help with this homework
Answers
Answer:
Step-by-step explanation:
use gauth math it helps with maths
You wish to test the following at a significance level of
.
You obtain a sample of size
in which there are 106 successful observations.
For this test, we use the normal distribution as an approximation for the binomial distribution.
For this sample...
The test statistic (
) for the data =
(Please show your answer to three decimal places.)
The p-value for the sample =
(Please show your answer to four decimal places.)
The p-value is...
greater than
less than (or equal to)
(Recall that when p(-value) is low, the null must go; when p(-value) is high, the null must fly)
Base on this, we should ....
fail to reject the null hypothesis
accept the null hypothesis
reject the null hypothesis
As such, the final conclusion is that...
The sample data suggest that the population proportion is significantly greater than 0.59 at the significant level of
= 0.01.
The sample data suggest that the population proportion is not significantly greater than 0.59 at the significant level of
= 0.01
Answers
The sample data suggest that the population proportion is not significantly greater than 0.59 at the significant level of 0.01.
How to explain the sampleIn this case, the test statistic is calculated as follows:
z = (106/150 - 0.59) / sqrt(0.59(1-0.59)/150)
= 1.55
The p-value is calculated as the area under the standard normal curve to the right of the test statistic. In this case, the p-value is calculated as follows:
p-value = p(Z > 1.55)
= 0.123
Since the p-value is greater than the significance level of 0.01, we fail to reject the null hypothesis. Therefore, we cannot conclude that the population proportion is significantly greater than 0.59 at the significant level of 0.01.
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A jar contains 8 pennies, 3 nickels, 5 dimes, and 2 quarters. If one coin is chosen from the jar, how many ways are there to get more than 4 cents
Answers
Answer: The jar contains a total of 18 coins (8 pennies + 3 nickels + 5 dimes + 2 quarters). To get more than 4 cents, we need to choose a nickel, dime, or quarter. There are 3 nickels, 5 dimes, and 2 quarters, for a total of 10 coins that satisfy this condition. Therefore, there are 10 ways to choose a coin from the jar that is more than 4 cents.
Select ALL TRUE statements
A) There are no zeroes
B) There is one zero
C) There are two zeroes
D) The vertex is (1, 14)
E) The vertex is (14, 1)
F) The vertex is (2, 14)
G) The vertex is (14, 2)
H) The axis of symmetry is x = 1
I) The axis of symmetry is x = 2
J) The "a" of the parabola is positive
K) The "a" of the parabola is negative
M) The parabola has a minimum
N) The parabola has a maximum
O) The zeroes are -2 and 6
P) The zeroes are 1 and 6
Q) The zero is 6
R) The zero is 14
Answers
Answer:
The correct statements are:
A) There are no zeroes
D) The vertex is (1, 14)
H) The axis of symmetry is x = 1
J) The "a" of the parabola is positive
M) The parabola has a minimum
Therefore, the options B, C, E, F, G, I, K, N, O, P, Q, and R are all false.
Step-by-step explanation:
Step-by-step explanation:
Remember that, this is quadratic function graph.
Let's analyze fact the graph. We get :
There are two roots/zeroes
Two roots are x1 = -2 , x2 = 6
Vertex is maximum value of parabola (2,14)
Symmetry function is x = 2 (you can show that, x-axis from vertex)
"a" parabola indicated negative
The parabola with "a" negative, thus have maximum value (show that vertex is (2,14))
Conclusion :
The true statements are C,F,I,K,N,O (6 statements are shown)
Subject : Mathematics
Level : JHS
Chapter : Quadratic Functions
please answer i would appreciate it thank you
Answers
a) The triangles are congruent by the AAA criterion.
b) The triangles are congruent by the SAS criterion.
a) In the first triangle the interior angles are 40 degrees and 30 degrees.
The other interior angle would be 180 - (40 + 30) = 110 degrees.
As per the diagram, the triangles have equal proportionate-sized side lengths.
Therefore, the triangles are congruent by the AAA criterion.
b) Both the triangles are right triangles and their adjacent side is 2 and the hypotenuse side is 4 centimeters.
Therefore, the triangles are congruent by the SAS criterion.
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Eight fourths is proportional to what value?
Answers
Eight fourths is proportional to the value of 2/1
What is proportionality of values?Proportionality of values means the relationship that exists between two variables where their ratios are equivalent to each other.
A ratio that is made up of two variables is said to be proportional to another ratio when after being simplified one arrives at the same ratio.
Using the 8:4 or 8/4. This is equivalent to 2/1 and also equivalent to 16/8 as the simplification leads to 2/1
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Find the surface area and volume of the for fire. Round to the nearest tenth
Answers
The surface area and the volume of the cone is 150.8 in², 116. 1in³. option A
How to determine the valuesThe formula for calculating the surface area of a cone is expressed as;
SA = πr² + πrl
Such that the parameters are;
r is the radius l is the lengthSubstitute the values, we have;
Surface area= 3.14 × 16 = 3.14 × 4 × 8
Multiply the values
Surface area = 50.24 + 100.48
Add the values
Surface area = 150.8 in²
Volume of the cone is;
Volume = 3.14 × 4² × 6.9/3
Volume = 3.14 × 16 × 6.9/3
Volume =116. 1in³
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help me solve my math
Answers
Answer:
653.3 bacteria
Step-by-step explanation:
A continuously growing population of bacteria is modeled by the function:
[tex]P(t) = P_0 \cdot e^{rt}[/tex]
where:
[tex]P(t)[/tex] is the population after [tex]t[/tex] time periods[tex]P_0[/tex] is the initial population[tex]r[/tex] is the relative rate of growthIn this problem, we are given the following values:
[tex]P_0 = 484 \text{ bacteria}[/tex][tex]r = 15\% = 0.15[/tex][tex]t = 2[/tex]We can plug these into the function to solve for [tex]P(2)[/tex].
[tex]P(t) = P_0 \cdot e^{rt}[/tex]
[tex]P(2) = 484 \cdot e^{(0.15 \, \cdot \, 2)}[/tex]
[tex]P(2) = 484 \cdot e^{0.3}[/tex]
Finally, the right side of this equation can be evaluated using a calculator to solve for the population of the bacteria after 2 hours.
[tex]\huge{\text{P(2) = 653.3 bacteria}}[/tex]
Given f(x) = x³ - 6x + k, and the remainder when f(x) is divided by x - 1 is 14, then what is the value of k?
Answers
Answer: 19
Step-by-step explanation: The best way is to set this up with synthetic division (as the attached image).
Hope this helps!
PLEASE HELP LOL
What is the value of x in this triangle?
Enter your answer in the box.
x =
Answers
The solution is: the value of x in this triangle is x = 83°.
Here, we have,
given that,
the angles of a triangle are:
44, 53 and x
now, we have to find the value of x in this triangle.
we know that,
Angle sum property of triangle states that the sum of interior angles of a triangle is 180°.
so, we have,
44 + 53 + x = 180°
or, x= 83
Hence, The solution is: the value of x in this triangle is x = 83°.
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A shirt manufacturer pays a worker $0.47 for each acceptable shirt inspected under the prescribed job description. If the worker had the following work record, find the gross earnings for the week: Monday, 250 shirts; Tuesday, 300 shirts; Wednesday, 178 shirts; Thursday, 326 shirts; Friday, 296 shirts
Answers
(250 shirts * 0.47) + (300 shirts * 0.47) + (178 shirts * 0.47) +
(326 shirts * 0.47) + (296 shirts * 0.47) =
$85.07
(0.47*670) = $85.07
Solve and graph. |3x+6/9|>=2
Answers
The solution to the inequality expression is -8/9 ≤ x ≥ 4/9
How to solve and graph the inequality expressionFrom the question, we have the following parameters that can be used in our computation:
|3x + 6/9| ≥ 2
Expand the inequality expression
So, we have
-2 ≤ 3x + 6/9 ≥ 2
Subtract 6/9 from both sides
So, we have
-24/9 ≤ 3x ≥ 12/9
Divide through the equation by 3
-8/9 ≤ x ≥ 4/9
Hence, the solution to the inequality expression is -8/9 ≤ x ≥ 4/9
The graph is attached
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6 sin θ=5 to the nearest 0.1°
Answers
The value of the equation 6 sinθ=5 for θ is 56.4 degrees
How to evaluate the equationFrom the question, we have the following parameters that can be used in our computation:
6 sinθ=5
Express the equation properly
So, we have the following representation
6 sin(θ) = 5
Divide both sides of the equation by 6
This gives
sin(θ) = 5/6
Evaluate the quotient
sin(θ) = 0.833
Take the arc sin of both sides
θ = sin⁻¹(0.833)
Evaluate
θ = 56.4
Hence, the value of the equation for θ is 56.4 degrees
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Complete question
Approximate θ in the equation, to the nearest 0.1 degrees
6 sin(θ) = 5
