Answer:
[tex]\huge\boxed{\sf 38}[/tex]
Step-by-step explanation:
Given expression:= a³ + b (6 + c)
Put a = 2, b = 3 and c = 4
= (2)³ + 3 (6 + 4)
= 8 + 3(10)
= 8 + 30
= 38[tex]\rule[225]{225}{2}[/tex]
Answer:
Step-by-step explanation:
the requied answer is 38.
according to the question the value of a=2,b=3,c=4.
here,
to find the value of a³ + b (6 + c)we have to do it in steps:
step 1: solve the bracket (6+4) =10.
step 2: solve the value of a³ =8.
now put these values ,
=8+3(10)
=38.
-10-9-8-7-6-5-4-3-2-1 0 1 2 3 4 5 6 7 8 9 10
Which of the following inequalities is represented by the number line?
A) x > 4.5
B) x ≥ 4.5
OC) x < 4.5
D) x ≤ 4.5
Answer:
The Correct answer is B
x≥4.5
Which choice is equivalent to the product below? √3 times √5 times √6
An answer choice that is equivalent to the product below include the following: B. 3√10.
How to determine the equivalent product?In this scenario and exercise, you are required to determine the correct and most accurate answer choice that is equivalent to the product of the given mathematical expression.
In this scenario and exercise, the simplest form of the given expression √3 × √5 × √6 can be determined or calculated by simplifying it as follows;
Expression = √3 × √5 × √6
Expression = √3 × √5 × √(3 ×2)
Expression = √3 × √5 × √3 × √2
Expression = 3 × √(5 × 2)
Expression = 3 × √10
Expression = 3√10.
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Missing information:
The question is incomplete and the complete question is shown in the attached picture.
A group consists of men and women. people are selected to attend a conference.
a. In how many ways can people be selected from this group of ?
There are 715 ways to select four people from a group of six men and seven women to attend a conference.
What are combinations?Combinations in mathematics relate to the various ways that a group of things can be chosen, regardless of the order in which they are chosen. Combinations are a form of counting problem where a smaller subset of the objects in the bigger set are selected.
The combination is given by the formula:
C(n,r) = n!/(r!(n-r)!)
The total number of people = 13.
The number of ways we can choose 4 people from the given 13 people are:
C(13,4) = 13!/(4!9!) = (13x12x11x10)/(4x3x2x1) = 715
Hence, there are 715 ways to select four people from a group of six men and seven women.
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The complete question is:
A coffee shop offers an annual "Mug Club Membership" in which customers can purchase a mug for $75, then mug refills cost $1.95 each for the year. Find the total cost for a Mug Club member if they refill their cup 120 times in one year.
the total cost for a Mug Club member who refills their cup 120 times in one year is $309.
How to solve?
If a customer purchases a Mug Club membership, they pay $75 for the mug and then refill it for $1.95 per refill. If they refill their mug 120 times in one year, the total cost would be:
$75 (for the initial purchase of the mug) + $1.95 x 120 (for the 120 refills)
= $75 + $234
= $309
Therefore, the total cost for a Mug Club member who refills their cup 120 times in one year is $309.
Cost refers to the amount of money or resources that are required to produce or obtain a good or service. It can include expenses such as materials, labor, rent, utilities, and other expenses incurred in the production or acquisition of a product or service.
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Which of the following components should you look for when editing in speech rhetorical strategies main? Idea and supporting detail grammar and spelling errors level of formality
When editing a speech, you should look for these components:
rhetorical strategieslevel of formalitygrammar and spelling errorsmain idea and supporting details.What does editing a speech involves?The act of editing speech involves more than just correcting grammar and spelling errors as its also involves analyzing the rhetorical strategies used, ensuring that the level of formality is appropriate for the audience and occasion and making sure that the main idea and supporting details are clearly presented and organized.
An effective editing can help to strengthen the message of the speech and increase its impact on the audience. Therefore, it is important to consider all of these components when editing a speech.
Full question "Which of the following components should you look for when editing in speech rhetorical strategies main? Idea and supporting detail grammar and spelling errors level of formality"
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HELP WHATS THE ANSWER
The surface area covered with stickers is 169.4 cm².
How to calculate the surface area of the paperweight?
We need to find the area of each face and then add them up for calculate the surface area of the paperweight,
We know,
Area of the rectangular base [tex]= length \times breadth = 17 cm \times 11 cm = 187 \: {cm}^{2} [/tex]
Area of the triangular top = (1/2) x base x height = (1/2) × 15 cm × 8 cm × 7 cm / √((15/2)² - (8/2)²) = 42 cm²
Area of the front and back faces (which are rectangles) [tex]= 2 \times length \times height = 2 \times 17 cm \times 10 cm = 340 \: cm²[/tex]
Area of the left and right faces (which are trapezoids) [tex]= ( \frac{1}{2} )(a+b) \times h \times 2 = ( \frac{1}{2} )(15 cm + 8 cm) \times 7 cm \times 2 = 91 {cm}^{2} [/tex]
Area of the bottom face (which is a rectangle) [tex]= length \times breadth = 17 cm \times 11 cm = 187 cm²[/tex]
Total surface area = 187 cm² + 42 cm² + 340 cm² + 91 cm² + 187 cm² = 847 cm²
To find the surface area covered with stickers, we need to calculate 20% of the total surface area:
Surface area covered with stickers [tex]=20\% \: of \: 874 \: {cm}^{2} = 0.2 \times 847 \: {cm}^{2} = 169.4 \: {cm}^{2} [/tex]
Therefore, the surface area covered with stickers is 169.4 cm² approximately.
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Given the circle below with secants JKL and NML, find the length of JK. Round to the nearest tenth if necessary.
The length of JK is 42 units, which can be calculated using the theorem that states JK × JL = ML × JN, with the given lengths of KL, LM, and MN.
What is length?Length is a measurement of how long or extended an object or distance is, typically measured in units such as meters, centimeters, feet, or inches.
What is Theorem?A theorem is a statement or proposition that has been proven to be true through deductive reasoning or a mathematical proof, and is often used as a basis for further reasoning and conclusions.
According to the given information:
To find the length of JK, we can use the theorem which states that the product of the lengths of the segments of a secant is equal. In other words, JK × JL = ML × JN. We are given the lengths of KL, LM, and MN, and we know that KL + LM + MN = JL + JN.
We can use this information to solve for JK. First, we need to find JL and JN. We can do this by subtracting KL and MN from LM to get JL = LM - KL and JN = LM - MN. Substituting these values into the equation JK x (LM - KL) = KL × (LM - MN), we can solve for JK.
JK = (KL × (LM - MN)) / (LM - KL) = (14 × (17 - 14)) / (17 - 14) = 14 × 3 = 42.
Therefore, the length of JK is 42.
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3 The headmaster at a private school wants to
update the student dress code. He wishes to
survey a select group of parents of the students
enrolled at the school to determine their
opinion on the addition of a blazer to the school
uniform. Which method can be used to ensure
an unbiased sample is obtained for the survey?
A All parents attending the next PTO meeting
are surveyed.
B Every fifth person on a list of parent
volunteers is surveyed.
C All parents waiting in the pick-up line after
school are surveyed.
D All parents of students whose birthdays are
on even numbered days are surveyed.
(I will give brainliest if you proof your answer)
The best method to ensure an unbiased sample is to randomly select parents from the entire population of parents with enrolled students at the school.
To ensure an unbiased sample for the survey, the method used should not favor any particular group or exclude any group from the population.
Option A: Surveying all parents attending the next PTO meeting would not be an unbiased sample as not all parents attend PTO meetings.
Option B: Surveying every fifth person on a list of parent volunteers would also not be an unbiased sample as it may exclude parents who are not on the list.
Option C: Surveying all parents waiting in the pick-up line after school may not be an unbiased sample as it may exclude parents who do not pick up their children from school.
Option D: Surveying all parents of students whose birthdays are on even-numbered days may not be an unbiased sample as it excludes parents whose children's birthdays are on odd-numbered days.
Therefore, the best method to ensure an unbiased sample is to randomly select parents from the entire population of parents with enrolled students at the school.
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Question 2 of 5
The dance committee at Northeast Middle School is
choosing the theme for the spring dance. Members of the
committee conduct a poll to ask students about their
choices. They ask every 10th student entering the cafeteria
to complete a survey.
What is the sample in this study?
A. All students at Northeast Middle School
B. The students in the cafeteria
C. The students on the dance committee
D. The students who complete the survey
The sample in this study is D. The students who complete the survey.
This is because the dance committee is only collecting data from those students who are surveyed, which represents a smaller group within the entire population of the school.
The sample in this study refers to the specific group of individuals who are selected to participate in the survey or study.
In this case, the dance committee at Northeast Middle School is choosing the theme for the spring dance and conducts a poll to ask students about their choices.
They ask every 10th student entering the cafeteria to complete a survey.
Therefore, the sample in this study is the students who complete the survey.
They are the specific group of individuals who are selected to participate in the survey and provide information about their preferences for the spring dance theme.
D. The students who complete the survey.
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Answer:
The students who complete the survey
Step-by-step explanation:
Rewrite 5^/4. /2 as a single radical
O 10^/2^9
O10^/20^9
O9^/2^10
The expression can be rewriten as a single radical as:
[tex]\sqrt[5]{4} *\sqrt{2} = \sqrt[10]{2^9}[/tex]
How to rewrite the expression as a single radical?We want to rewrite the expression below as a single radical:
[tex]\sqrt[5]{4} *\sqrt{2}[/tex]
First remember that 4 = 2², then we can replace that to get:
[tex]\sqrt[5]{4} *\sqrt{2} = \sqrt[5]{2^2} *\sqrt{2}[/tex]
Converthing the roots to exponents we will get.
[tex]\sqrt[5]{2^2} *\sqrt{2} = 2^{2/5}*2^{1/2}[/tex]
Now the exponents are just added:
[tex]2^{2/5}*2^{1/2} = 2^{2/5 + 1/2} = 2^{4/10 + 5/10} = 2^{9/10} = \sqrt[10]{2^9}[/tex]
That is the correct option.
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A certain three-dimensional figure has one base and
3 faces.
The area of each face is the same.
The area of the base is 5 square centimeters.
The total surface area of the figure, including the base, is 26 square centimeters.
What is the area of one face of the three-dimensional figure?
7 is the area of one face of the three-dimensional figure .
What exactly is a three-dimensional figure?
Objects or shapes with three dimensions—length, breadth, and height—are referred to as three-dimensional objects or solid figures in geometry. The height of a three-dimensional object is the same as its thickness or depth, in contrast to a two-dimensional shape, which lacks height.
area of base = 5 cm²
total surface area = 26 cm²
26 = 3 * area of one face + 5
26 - 5 = 3 * area of one face
21/3 = 3 * area of one face
area of one face = 7
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one face of the three-dimensional figure has a surface area of 16/3 square centimeters.
What is surface area?The area is the space occupied by a two-dimensional flat surface. It is expressed in square units. The surface area of a three-dimensional object is the area occupied by its outer surface. It's also expressed in square units.
Let A represent the area of one of the three-dimensional figure's faces.
The overall surface area of the figure, including the base, is 26 square centimeters, according to the problem description. The total area of the base and the three similar faces is 26 - 5 = 21 square centimeters.
Because the three faces are identical, the total area of the three faces is 3A. As a result, we can write:
3A + 5 = 21
Subtraction of 5 from both sides yields:
3A = 16
By dividing both sides by three, we get:
A is equal to 16/3 square centimeters.
As a result, one face of the three-dimensional figure has a surface area of 16/3 square centimeters.
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what is the x and y coordinates of the vertex for f(x) = -2x^2 + 12x - 9
Answer:
The vertex of a quadratic function of the form f(x) = ax^2 + bx + c is located at the point (-b/2a, f(-b/2a)).
In this case, the quadratic function is f(x) = -2x^2 + 12x - 9, so we can use the formula above to find the coordinates of the vertex:
x-coordinate of vertex = -b/2a = -12/(2*(-2)) = 3
To find the y-coordinate of the vertex, we can evaluate the function at x = 3:
f(3) = -2(3)^2 + 12(3) - 9 = 9
Therefore, the coordinates of the vertex are (3, 9). The x-coordinate of the vertex is 3, and the y-coordinate of the vertex is 9.
What is the volume of a cube 12 inches by 12 inches and 12 inches high?
Answer: 1728 cubic meters
Step-by-step explanation: 12 x 12 x 12 V= LxWxH
Suppose you start with one liter of vinegar and repeatedly remove 0.14 L, replace with water, mix, and repeat. a. Find a formula for the concentration after n steps. b. After how many steps does the mixture contain less than 9% vinegar?
Formula for the concentration after n steps is [tex]C(n) = C(0) * (0.86)^n[/tex] and
after 11 steps, the mixture contains less than 9% vinegar.
What is concentration?
Concentration in science refers to the amount of a particular substance (the solute) that is dissolved in a given amount of a solution. It is typically expressed in units of moles per liter (M or mol/L) or as a percentage or fraction of the total solution.
a. Let C(n) be the concentration of vinegar after n steps. At each step, we remove 0.14 L of the mixture, which contains C(n) liters of vinegar. So we are left with (1 - C(n)) liters of water. We then add back 0.14 L of water, giving us a total volume of 1 liter. Therefore, the concentration after one step is:
[tex]C(1) = C(0) * \frac{1 - 0.14}{1}[/tex]
where C(0) is the initial concentration of vinegar, which is 1 liter per liter or 100%. After two steps, we repeat the process:
C(2) = C(1) * [tex]\frac{1 - 0.14}{1}[/tex]
Substituting the formula for C(1), we get:
C(2) = C(0) * [tex](\frac{1 - 0.14}{1}) * (\frac{1 - 0.14}{1})[/tex]
or, more generally:
[tex]C(n) = C(0) * (0.86)^n[/tex]
b. We want to find the smallest integer n such that C(n) < 0.09 or 9%. Substituting the formula from part (a), we get:
[tex]C(0) * (0.86)^n < 0.09[/tex]
Dividing both sides by C(0), we get:
[tex](0.86)^n < 0.09[/tex]
Taking the natural logarithm of both sides, we get:
n * ln(0.86) < ln(0.09)
Dividing both sides by ln(0.86), we get:
n > ln(0.09) / ln(0.86)
Using a calculator, we get:
n > 10.7
Since n must be an integer, the smallest possible value of n is 11. Therefore, after 11 steps, the mixture contains less than 9% vinegar.
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If the length and width of a rectangle are 11 cm and 10 cm, then find its perimeter. OA. 420 cm OB. 21 cm OC. 42 cm OD. 110 cm
Answer:
Perimeter = 42 cmStep-by-step explanation:
It is given that length and width of a rectangle is 11 cm and 10 cm.
We know the formula of Perimeter of rectangle
[tex]:\implies \: [/tex] Perimeter = 2(L + B)
Where 'L' denote the length of the rectangle and 'B' denotes the breadth of the Rectangle.
Now Let's substitute the value of Length= 11 cm and Breadth = 10 cm in the above formula .
[tex]:\implies \: [/tex] 2(11 + 10)
[tex]:\implies \: [/tex] 2 × 21
[tex]:\implies \: [/tex] 42 cm
Henceforth The perimeter of the rectangle is 42 cm
The perimeter of a rectangle is calculated by multiplying by 2 the sum of its length and width. So, in this case, the rectangle's perimeter is 42 cm.
Explanation:The subject of this question is on calculating the perimeter of a rectangle. The formula for finding the perimeter of a rectangle is 2*(length + width). Applying the values given, that is length = 11 cm and width = 10 cm.
So, the perimeter of a rectangle = 2*(11 + 10) cm = 2*21 cm = 42 cm
Therefore, the correct option is OC. 42 cm.
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If a surgery has a 92% change of being successful, what is the probability that a surgeon does 8 surgeries out of which 5 are successful?
According to probability, the answer to the question is that an average surgeon performs 8 operations, of which 5 are successful. 18.9%.
What is Binomial probability?In a fixed number of independent trials, each of which can only have one of two outcomes—success or failure—the number of successes is expressed as a probability distribution known as a binomial probability. Additionally, it is presummated that each trial has an equivalent chance of success.
The binomial probability formula can be used to determine the likelihood that a surgeon will perform 5 successful operations out of 8 given that each operation has a 92% chance of being successful.
You may find the binomial probability formula by using:
[tex]P(X = k) = C(n, k)*p^k*(1 - p)^{(n - k)}[/tex]
Where:
P(X = k) is the likelihood that, out of n surgeries, exactly k will be successful.
The binomial coefficient, C(n, k), is defined as the number of ways to select k successful operations among n surgeries C(n, k) = n! / (k! * (n - k)!), where ! denotes factorial.
p is the likelihood that a single surgery will succeed (92% in this case, or 0.92).
The number of successful operations that interests us is k.
The total number of operations is n, which in this case is 8.
By entering the values, we can determine the probability using the formula below:
P(X = 5) = C(8, 5) * 0.92⁵ * (1 - 0.92)⁽⁸⁻⁵⁾
C(8, 5) = 8! / (5! * (8 - 5)!) = 56
0.92⁵ = 0.659
(1 - 0.92)³ = 0.512
P(X = 5) = 56 * 0.512 * 0.659 = 18.89 or 18.9%
Given a 92% success rate for each surgery, the likelihood that a surgeon will perform 5 successful operations out of 8 is roughly 18.9%.
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For the winter clothing drive, Jada's class collected 7 2/3 pounds of clothing. Wesley's class collected 1 5/6 times as much clothing as Jada's class. How many pounds of clothing did Wesley's class collect?
Write your answer as a fraction or as a whole or mixed number.
Wesley's class collected 253/18 pounds of clothing, which can also be written as 14 1/18 pounds (rounded to the nearest hundredth).
What is a whole number example?Whole numbers include natural numbers that begin from 1 onwards. Let us look at some examples of whole numbers. The set of whole numbers is denoted by the alphabet 'W'. W = {0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10,.…}
Jada's class collected 7 2/3 kilograms of clothes. Wesley's class collected 15/6 times as many clothes as Jada's class, which means they collected:
1 5/6 x (7 2/3) pounds of fabric
To multiply fractions, you can first convert the mixed numbers to improper fractions, then multiply the numerators and denominators separately and simplify if possible.
Convert mixed numbers to improper fractions:
7 2/3 = (37 + 2)/3 = 23/3
1 5/6 = (61 + 5)/6 = 11/6
Multiply Fractions:
(11/6) * (23/3) = (1123)/(63) = 253/18
Therefore, Wesley's class collected 253/18 pounds of clothing, which can also be written as 14 1/18 pounds (rounded to the nearest hundredth).
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Select all the true statements about
the function h(x) = x/3 + 7 .
A. When x = 3, h(x) = 16.
B. When x = 4, h(x) = 8 1/3.
C. When x = 9, h(x) = 10.
D. When x = 10, h(x) = 10 1/3.
E. When x = 12, h(x) = 12.
Answer:
A. When x = 3, h(x) = 16 is false.
B. When x = 4, h(x) = 8 1/3 is true.
C. When x = 9, h(x) = 10 is true.
D. When x = 10, h(x) = 10 1/3 is true.
E. When x = 12, h(x) = 12 is false.Therefore, the true statements are B, C, and D.
What unit of measurement would you use to weigh an elephant? A Ounce B Ton C Millimeter D Pound
Answer:
B
Step-by-step explanation:
The unit of measurement that would typically be used to weigh an elephant is the ton. Elephants are very large animals, and they can weigh several tons, depending on their species and size. While other units of measurement like pounds, kilograms, or ounces could also be used to measure the weight of an elephant, the ton is the most appropriate unit for such a large animal.
what is angle NSR equal to?
The measure of the angle NSR is equal to 113 degrees
Calculating what is angle NSR equal to?From the question, we have the following parameters that can be used in our computation:
The circle
Using the angle of intersecting chords theorem, we have following equation
NSR = 1/2(Sum of major and minor arcs NS)
So, we have
NSR = 1/2 * (176 + 50)
Evaluate
NSR = 113
Hence, the angle is 113 degrees
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The Question is below ⬇️
Answer:
63
Step-by-step explanation:
given the sight of the angle it should be 63, correct me if I'm wrong.
im confused can someone explain step by step please
Find the direction of this
vector:
174 M
88.4 m
Remember, angles are measured from
the +x-axis.
direction (deg)
The direction of the vector is 27 degrees
How to find the vectorThe vector is the hypotenuse and the angle showing magnitude and direction.
To find the length of the hypotenuse of a right triangle, we can use the Pythagorean theorem.
hypotenuse^2 = opposite^2 + adjacent^2
hypotenuse^2 = 88.4^2 + 174^2
hypotenuse ≈ 195.17 m
Therefore, the magnitude of the vector (hypotenuse of the right triangle) is approximately 194.8 m.
The direction
We can use the trigonometric function of tangent to find the angle between the opposite and adjacent sides of a right triangle.
tan(θ) = opposite/adjacent
We are given
the opposite side as 88.4 m and the adjacent side as 174 mso we can use these values to find the angle θ:
tan(θ) = 88.4/174
θ = arc tan (88.4/174)
θ ≈ 26.93 degrees
Therefore, the angle between the opposite and adjacent sides of the right triangle is approximately 27 degrees.
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A bus traveled on a level road for 4 hours at an average speed 20 miles per hour faster than it traveled on a winding road. The time spent on the winding road was 4 hours. Find the average speed on the level road if the entire trip was 400 miles.
Answer:
Let's call the speed of the bus on the winding road "s". Then we know that the bus traveled at a speed of "s + 20" on the level road. We also know that the time spent on the winding road was 4 hours, so the distance traveled on the winding road is:
distance = speed × time = s × 4
Similarly, the distance traveled on the level road is:
distance = speed × time = (s + 20) × 4
Since the entire trip was 400 miles, we can write:
4s + 4(s + 20) = 400
Simplifying this equation, we get:
8s + 80 = 400
8s = 320
s = 40
Therefore, the speed of the bus on the winding road was 40 mph, and the speed on the level road was 40 + 20 = 60 mph.
To check that this solution is correct, we can calculate the distance traveled on each road:
distance on winding road = 40 × 4 = 160 miles
distance on level road = 60 × 4 = 240 miles
The total distance traveled is indeed 160 + 240 = 400 miles, so our solution is correct.
Therefore, the average speed on the level road was 60 miles per hour.
Drag each tile to the correct location on the table. Each tile can be used more than once but not all tiles will be used. Choose the justification for each step in the solution to the given equation.
The value of x from the given equation is 8/15.
The given equation is 17/3 - 3/4 x= 1/2 x+5
17/3 - 3/4 x= 1/2 x+5 (Given)
17/3 - 3/4 x -17/3= 1/2 x+5 -17/3 (Subtraction property of equality)
-3/4 x = 1/2 x -2/3
-3/4 x -1/2 x = 1/2 x -2/3 -1/2 x (Subtraction property of equality)
-5/4 x=-2/3
-5/4 x × 4/5=-2/3 × 4/5 (Multiplication property of equality)
x= 8/15
Therefore, the value of x from the given equation is 8/15.
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Manny bought a brand new car in 2012 for $28,750. If the car depreciates by 12% each year, write an exponential function to model the situation, then find the value of the car in 2018. please round to two decimal places.
note use formula f(t)=a(1+r)^t
Therefore, the value of the car in 2018 was approximately $13,197.36. Rounded to two decimal places, this is $13,197.36.
What is decimal?A decimal is a way of representing a number that is based on powers of ten. It is a number expressed in the base-ten system, which means that each digit in the number represents a power of 10. The decimal point separates the whole number part of the decimal from the fractional part of the decimal.
To model the depreciation of the car over time, we can use the formula:
f(t) = a(1 - r)^t
where:
After t years, f(t) is the car's worth.
a is the initial value of the car, which is $28,750.
r is the annual depreciation rate, which is 12% or 0.12 (expressed as a decimal).
t represents how long it has been since the car been acquired.
Substituting the given values, we get:
f(t) = 28,750(1 - 0.12)^t
To find the value of the car in 2018, we need to substitute t = 6 (since 2018 is 6 years after 2012) and evaluate the function:
f(6) = 28,750(1 - 0.12)^6
Simplifying,
f(6) = 28,750(0.88)^6
Evaluating using a calculator, we get:
f(6) ≈ 13,197.36
Therefore, the value of the car in 2018 was approximately $13,197.36. Rounded to two decimal places, this is $13,197.36.
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The value of the car in 2018 was approximately $14,303.22.
What is exponential functions?
An exponential function is a mathematical function of the form f(x) = [tex]a^{x}[/tex], where a is a positive constant and x is the input variable. The base a is usually a positive real number, but it can also be a complex number.
The initial value of the car is $28,750, and it depreciates by 12% each year. This means that the value of the car after t years can be modeled by the exponential function:
f(t) = [tex]28750(1 - 0.12)^{t}[/tex]
Simplifying the expression inside the parentheses:
f(t) = [tex]28750(0.88)^{t}[/tex]
To find the value of the car in 2018, we need to substitute t = 6, since 2018 is 6 years after 2012:
f(6) = [tex]28750(0.88)^{6}[/tex]
Using a calculator, we get:
f(6) = [tex]28750(0.497^{1})[/tex]
f(6) = 14,303.22
Therefore, the value of the car in 2018 was approximately $14,303.22.
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If c is the least common multiple of A and B, which must be trye?
A. c b and c>a
D. c≥b and c≥a
The statement that must be true is c is the least common multiple of A and B, is D. c ≥ b and c ≥ a.
Why is this so ?The rationale behind this lies in the fact that finding the least common multiple (LCM) of two numbers necessitates determining a value that is commensurate with both figures, yet simultaneously represents their most diminutive shared multiple.
To expound further, It is the minimal positive integer among all feasible ones that can be divided entirely without any leftover remainder by all supplied integers. Thus, this computation allows you to determine the minimum possible factorization required to obtain each number while preserving its numerical integrity.
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1. The ratio of faculty members to students at a college is 1:18. If there are 16000 students, how many faculty members are there? Round to the nearest whole number
Therefore, there are approximately 889 faculty members at the college.
What is ratio?Ratio is a mathematical concept that expresses the relationship between two or more quantities or values. It is a way to compare the size of two numbers, by dividing one number by the other. The result of this division is a numerical expression of the relative size of the two numbers.
Ratios are often expressed as a fraction or a colon (:) between the two numbers. For example, if there are 4 red balls and 6 blue balls in a bag, the ratio of red balls to blue balls can be expressed as 4/6 or 4:6. This means that for every 4 red balls in the bag, there are 6 blue balls.
Ratios are commonly used in various fields, such as finance, statistics, and science, to compare different values and make meaningful interpretations.
To solve this problem, we need to use the ratio between faculty members and students, which is given as 1:18. This means that for every one faculty member, there are 18 students.
If there are 16000 students in the college, we can find the number of faculty members by dividing the number of students by the ratio of students to faculty members:
Number of faculty members = 16000 / 18
This gives us 888.888, but since we are asked to round to the nearest whole number, we should round up to 889. Therefore, there are approximately 889 faculty members at the college.
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Which of these expressions is equivalent to log (46)?
OA. log (6) log (4)
OB. log (6) - log (4)
OC. 6. log (4)
OD. log (6) + log (4)
Answer: the answer is B
Step-by-step explanation:
A rocket is launched in the air. Its height in feet is given by ℎ ( � ) = − 16 � 2 + 144 � h(t)=−16t 2 +144t where � t represents the time in seconds after launch. What is the rocket’s greatest height?
The calculated value of the rocket’s greatest height is 324 feet
Calculating the rocket’s greatest height?From the question, we have the following parameters that can be used in our computation:
h(t) = -16t² + 144t
Differentiate the height function and set the differentiated equation to 0
So, we have
32t = 144
This gives
t = 144/32
So, we have
t = 4.5
Substitute t = 4.5 in the above equation, so, we have the following representation
h(4.5) = -16(4.5)^2 + 144(4.5)
Evaluate
h(4.5) = 324
Hence, the rocket’s greatest height is 324 feet
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Complete question
A rocket is launched in the air. Its height in feet is given by h(t) = −16t² + 144t where t represents the time in seconds after launch.
What is the rocket’s greatest height?
