"At least one digit is present to the left of the decimal point in all cases" and "the exponent can be a positive or negative integer" are the correct option for the given question.
Decimal numbers, also known as base-10 numbers. They use a system of digits from 0 to 9 and a decimal point to represent values. The decimal point separates the integer part of the number from the fractional part.
For example, in the decimal number 56.36, 56 is the integer part and 36 is the fractional part.
Hence, at least one digit is present to the left of the decimal point in all cases.
In scientific notation, the exponent is used to represent very large or very small numbers. The number is written in the form of a x [tex]10^n[/tex] where 'a' is a decimal number between 1 and 10 (inclusive) and 'n' is an integer (positive or negative) exponent.
Say, for example, 0.00006 can be written as 6 x [tex]10^{-5}[/tex] where 6 is the coefficient and -5 is the exponent.
Read more about Decimal numbers:
brainly.com/question/29622901
#SPJ4
CURRENT OBJECTIVE
Using proportions to compare
Question
Georgia has 401 golf courses with a population of 10, 736, 059 while New Hampshire has 113
golf courses with a population of 1, 371, 246. If New Hampshire was proportional to Georgia in
golf courses to population, how many golf courses would New Hampshire have? Round to the
nearest whole number.
Provide your answer below:
golf courses
And why when I scan it gives me everything but what I ask for
With constant of proportionality= 0.45 the New Hamsphire would have 51 golf courses.
What is a constant of proportionality?
The constant of proportionality is the constant value of the ratio between two proportional quantities. Two varying quantities are said to be in a relation of proportionality when, either their ratio or their product yields a constant. The value of the constant of proportionality depends on the type of proportion between the two given quantities: Direct Variation and Inverse Variation.
Direct Variation: The equation for direct proportionality is y = kx, which shows as x increases, y also increases at the same rate. Example: The cost per item(y) is directly proportional to the number of items(x) purchased, expressed as y ∝ x
Inverse Variation: The equation for the indirect proportionality is y = k/x, which shows that as y increases, x decreases and vice-versa. Example: The speed of a moving vehicle (y) inversely varies as the time taken (x) to cover a certain distance, expressed as y ∝ 1/x
In both cases, k is constant. The value of this constant is called the coefficient of proportionality. The constant of proportionality is also known as the unit rate.
Now,
As given Georgia has 401 golf courses with a population of 10, 736, 059 while New Hampshire has 113 golf courses with a population of 1, 371, 246.
So Georgia have 1 golf course for 26773 people and New hamsphore have 1 golf course for 12135 people.
that means they have constant of proportionality= 0.45 with respect to population/golf course ratio .
population/golf course ratio for georgia=26773
population/golf course ratio for new hamsphire=12135
and For new hamsphire to have same ratio for population/golf ratio as georgia it will need 113*0.45=51 golf courses
To know more about constant of proportionality visit the link
https://brainly.com/question/29126727?referrer=searchResults
#SPJ1
The height in feet of a firework t seconds after it is launched is modeled by h(t) --16r2 + 105t + 10. Find its average speed from l to 3 seconds.
The change in height divided by the change in time yields the firework's average speed from t=1 to t=3 seconds.
Average change speed is equal to (h(3) – h(1)) (3 - 1)
h(3) = 16*32 + 105*3 + 10 = 536
h(1) = 16*12 + 105*1 + 10 = 126
Average speed = (536 - 126)/(3 - 1) = 410/2 = 205 ft/sec
h(t) = 16r2 + 105t + 10 models the height of a firework t seconds after it is released. We must determine the change in height divided by the change in time in order to get its average speed between t=1 and t=3 seconds.
By entering t = 3 into h(t), we can determine the height at 3 seconds, which gives us h(3) = 16*32 + 105*3 + 10 = 536. We can figure out the height.
Learn more about average here
https://brainly.com/question/24057012
#SPJ4
Attend to Precision Denise needs 4 pounds of soil
to fill a flowerpot. She has a bag with 2 1/3 pounds of soil
and a box with 1 3/4 pounds of soil. Does Denise have enough
soil to fill the flowerpot? Explain.
Yes, she does have the enough soil as she needs 4 pounds of soil.She have [tex]7 \frac{5}{12}[/tex] pound of soil.
What is Fraction?
An element of a whole is a fraction. The number is represented mathematically as a quotient, where the numerator and denominator are split. Both are integers in a simple fraction. A fraction appears in the numerator or denominator of a complex fraction. The numerator of a proper fraction is less than the denominator.
What is BODMAS?
The abbreviation BODMAS was created to aid kids in remembering the right order to carry out mathematical operations when solving problems. B-Brackets, O-Orders (powers/indices or roots), D-Division, M-Multiplication, A-Addition, and S-Subtraction are all abbreviated as Bodmas.
Given that;
She has
⇒ [tex]2\frac{1}{3} + 1\frac{3}{4}[/tex]
⇒ 17/3 + 7/4
⇒ [tex]\frac{17*4 + 7 *3}{12}[/tex]
⇒ 68 + 21 /12
⇒ 89/12
⇒ [tex]7 \frac{5}{12}[/tex]
So, She has [tex]7 \frac{5}{12}[/tex] pound of soil and she need 4 pounds only.
Hence, Denise have enough soil to fill the flower plot.
Learn more about Fraction click here:
https://brainly.com/question/17220365
#SPJ1
which of the statements best describes a bar graph? data are presented with bars that are proportional in height to the measured value. continuous data are presented as dots that are placed at specific x- and y-coordinates. categories of data are presented with sections of a circle that are proportional in size to the measured value. data points are scattered across the graph at specific x- and y-coordinates.
The tatment which describe best a bar graph is data are presented with bars that are proportional in height to the measured value.
Let us know more about a bar graph .
The pictorial representation of grouped data, in the form of vertical or horizontal rectangular bars, where the lengths of the bars are equivalent to the measure of data, are known as bar graphs or bar charts.
The bars drawn are of uniform width, and the variable quantity is represented on one of the axes. Also, the measure of the variable is depicted on the other axes. The heights or the lengths of the bars denote the value of the variable, and these graphs are also used to compare certain quantities. The frequency distribution tables can be easily represented using bar charts which simplify the calculations and understanding of data.
The three major attributes of bar graphs are:
1) The bar graph helps to compare the different sets of data among different groups easily.
2) It shows the relationship using two axes, in which the categories are on one axis and the discrete values are on the other axis.
3) The graph shows the major changes in data over time.The bar graphs can be vertical or horizontal. The primary feature of any bar graph is its length or height. If the length of the bar graph is more, then the values are greater than any given data.
Bar graph normally show categorical and numeric variables arranged in class intervals. They consist of an axis and a series of labelled horizontal or vertical bars. The bars represent frequencies of distinctive values of a variable or commonly the distinct values themselves. The number of values on the x-axis of a bar graph or the y-axis of a column graph is called the scale.
The types of bar charts are as follows:
Vertical bar chart
Horizontal bar chart
Even though the graph can be plotted using horizontally or vertically, the most usual type of bar graph used is the vertical bar graph. The orientation of the x-axis and y-axis are changed depending on the type of vertical and horizontal bar chart. Apart from the vertical and horizontal bar graph, the two different types of bar charts are:
Grouped Bar Graph
Stacked Bar Graph
To know more about bar graph :
https://brainly.com/question/30355989
#SPJ4
The statment which describe best a bar graph is data are presented with bars that are proportional in height to the measured value.
Let us know more about a bar graph .
The pictorial representation of grouped data, in the form of vertical or horizontal rectangular bars, where the lengths of the bars are equivalent to the measure of data, are known as bar graphs or bar charts.
The bars drawn are of uniform width, and the variable quantity is represented on one of the axes. Also, the measure of the variable is depicted on the other axes. The heights or the lengths of the bars denote the value of the variable, and these graphs are also used to compare certain quantities. The frequency distribution tables can be easily represented using bar charts which simplify the calculations and understanding of data.
The three major attributes of bar graphs are:
1) The bar graph helps to compare the different sets of data among different groups easily.
2) It shows the relationship using two axes, in which the categories are on one axis and the discrete values are on the other axis.
3) The graph shows the major changes in data over time.The bar graphs can be vertical or horizontal. The primary feature of any bar graph is its length or height. If the length of the bar graph is more, then the values are greater than any given data.
Bar graph normally show categorical and numeric variables arranged in class intervals. They consist of an axis and a series of labelled horizontal or vertical bars. The bars represent frequencies of distinctive values of a variable or commonly the distinct values themselves. The number of values on the x-axis of a bar graph or the y-axis of a column graph is called the scale.
The types of bar charts are as follows:
Vertical bar chart
Horizontal bar chart
Even though the graph can be plotted using horizontally or vertically, the most usual type of bar graph used is the vertical bar graph. The orientation of the x-axis and y-axis are changed depending on the type of vertical and horizontal bar chart. Apart from the vertical and horizontal bar graph, the two different types of bar charts are:
Grouped Bar Graph
Stacked Bar Graph
To know more about bar graph :
brainly.com/question/10666484
#SPJ4
NO LINKS!!
45. Express 3log₅x + log₅y - 2log₅w as a single logarithm
46. Find the missing value: log21 -2log7 + log28 = log__
47. Expand ln[(x - 4)(2x+5)²]
Answer:
[tex]\textsf{45.} \quad \log_5\left(\dfrac{x^3y}{w^2}\right)[/tex]
[tex]\textsf{46.} \quad \log 12[/tex]
[tex]\textsf{47.} \quad \ln(x-4)+2\ln(2x+5)[/tex]
Step-by-step explanation:
[tex]\boxed{\begin{minipage}{8cm}\underline{Log laws}\\\\Product law:\quad\:$\log_axy=\log_ax + \log_ay$\\\\Quotient law:\;\;\;$\log_a \left(\dfrac{x}{y}\right)=\log_ax - \log_ay$\\\\Power law:\quad\;\;\;\:$\log_ax^n=n\log_ax$\\\end{minipage}}[/tex]
Question 45[tex]\begin{aligned}3\log_5x + \log_5y - 2\log_5w&=\log_5x^3 + \log_5y - \log_5w^2\\&=\log_5\left(x^3 \cdot y\right)- \log_5w^2\\&=\log_5\left(\dfrac{x^3y}{w^2}\right)\end{aligned}[/tex]
Question 46[tex]\begin{aligned}\log21 - 2 \log7 + \log28 &=\log21 - \log7^2 + \log28\\&=\log21 - \log49 + \log28\\&=\log\left(\dfrac{21}{49}\right) + \log28\\&=\log\left(\dfrac{3}{7} \cdot 28\right)\\&=\log\left(\dfrac{84}{7}\right)\\&=\log12\end{aligned}[/tex]
Question 47[tex]\begin{aligned}\ln \left[(x - 4)(2x+5)^2\right]&=\ln(x-4)+\ln(2x+5)^2\\&=\ln(x-4)+2\ln(2x+5)\\\end{aligned}[/tex]
How do you use the definition of continuity and the properties of limits to show that the function h(t)=(2t-3t²)/(1+t³) is continuous at the given number a=1?
The function h(t) = (2t - 3t²)/(1 + t³) is continuous at x = 1, as the limit exists and is equals to the numeric value of the function.
What is the continuity concept?A function f(x) is continuous at x = a if it is defined at x = a, and the lateral limits are equal to the numeric value of the function, that is:
[tex]\lim_{x \rightarrow a^-} f(x) = \lim_{x \rightarrow a^+} f(x) = f(a)[/tex]
The function is defined as follows:
h(t) = (2t - 3t²)/(1 + t³)
At t = 1, the first step is trying to obtain the limit as the numeric value, hence:
h(1) = (2 - 3)/(1 + 1) = -1/2.
As the limit does not result in an undetermined result, the limit exists, is equals to the numeric value of the function, the function is continuous at x = 1.
More can be learned about the continuity of a function at https://brainly.com/question/24637240
#SPJ1
The jazz band has b members. To raise money for a tour,each member sold 12 raffle tickets. Write an expression that shows the number of the raffle tickets sold answer
Answer:
m=12b
Step-by-step explanation:
m (money raised) is equal to 12b, or 12 tickets per b (b = people)
Word Needed! *
The Bellah's pool is leaking. The pool leaked 3/4
gallon in 20 minutes, or 1/3hour. How many
gallons is the pool leaking each hour?
There are 13 purple flowers. There are nine pink flowers. How many more purple flowers are there?
Answer:4
Step-by-step explanation:
13-9=4
if you are subtracting 9 add more than the number. for example, 17-9=8
8 is one more than the number 7 in 17.
Solve for x.
12
10
X
5
will give brainliest!!
Answer:
x=60
Step-by-step explanation:
Robin paid a $120 a month on a credit card. She was late on a payment so her monthly bill was raised to $150 a month. which of these shows how Robin can calculate the percent increase she was charged
Answer: One way to calculate the percent increase in Robin's monthly bill is to use the following formula:
% increase = (new amount - original amount) / original amount x 100
In this case, the original amount is $120 and the new amount is $150. So, the calculation would be:
% increase = (150 - 120) / 120 x 100 = 30 / 120 x 100 = 0.25 x 100 = 25
Therefore, the percent increase in Robin's monthly bill is 25%.
Another way to calculate the percent increase is to use the formula:
(New amount - original amount) / original amount
In this case: (150-120)/120 = 0.25, and multiply by 100 to get 25%
So, both formula gives the same answer 25%
Step-by-step explanation:
Which of the following are properties of a kite? Choose ALL that apply.
Diagonals are perpendicular
Two pairs of consecutive sides are congruent
1 diagonal bisects the other
Opposite angles are congruent
Answer:
Diagonals are perpendicular
1 diagonal bisects the other
Opposite angles are congruent
the pressure gauge on a cylinder of gas registers the gauge pressure, which is the difference between the interior pressure and the exterior pressure p0. let's call the gauge pressure pg. when the cylinder is full, the mass of the gas in it is mi at a gauge pressure of pgi. assuming the temperature of the cylinder remains constant, show that the mass of the gas remaining in the cylinder when the pressure reading is pgf is given by mf
The gauge pressure, or the difference between the inner pressure and the external pressure p0, is what the pressure gauge on a gas cylinder measures. Give the gauge pressure the letter pg.
The gas in the cylinder weighs mi at pgi gauge pressure when it is full. We can apply the ideal gas formula, PV = nRT, where P is pressure, V is volume, n is the number of moles, R is the ideal gas constant, and T is temperature, assuming the cylinder's temperature stays constant.
We can assume that the product nRT is constant because the temperature is constant. Consequently, we can write:
(pgf + p0) = (pgi + p0)(Vi) (Vf)
where Vi is the cylinder's initial volume and Vf is the cylinder's final volume when the pressure is pgf.
We also know that the gas's mass, m, is determined by multiplying the number of moles, n, by the molar mass, M, or m = nM.
The ideal gas law can be used to express the number of moles in terms of volume and pressure:
m/M = P(V/RT) = n
Thus, mf = pgf(Vf/RT).
M equals (pgf + p0)(Vf/RT).
(Vi/RT) Mi (pgi + p0)
where mf is the mass of gas still present in the cylinder at pgf pressure.
To learn more about the ideal gas equation, refer to the link:brainly.com/question/28837405
#SPJ4
You flip a coin 16 times and get heads 7 times. Based on this experiment, what is the probability of flipping a coin and getting heads?
The probability of flipping a coin and getting heads is 7/16
How to determine the probability of flipping a coin and getting heads?from the question, we have the following parameters that can be used in our computation:
Number of flips = 16
Number of heads = 7
The probability is then calculated as
P = Head/Flips
substitute the known values in the above equation, so, we have the following representation
P = 7/16
Hence, the probability is 7/16
Read more about probability at
https://brainly.com/question/251701
#SPJ1
during one period a bakery rejected 372 items as unfit for sale in the following period the bakery rejected only 323 items a decrease in unfit bakery items what is the percent decrease
Answer:
To calculate the percent decrease in the number of rejected items, we can use the following formula:
Percent decrease = ((initial value - final value) / initial value) x 100
In this case, the initial value is 372 (the number of items rejected in the first period) and the final value is 323 (the number of items rejected in the second period).
So, the percent decrease is:
((372 - 323) / 372) x 100 = 13.1%
Therefore, there is a 13.1% decrease in the number of rejected items from the first period to the second period.
A bird of species A, when diving, can travel 6 times as fast as a bird of species B top speed. If the total speeds for these two birds is 238 miles per hour, find the fastest speed of the bird of species A and the fastest speed of the bird of species B.
Answer: Bird A's top speed is 1428 MPH.
Step-by-step explanation: 238x6 = 1428
Graph the following system of inequalities.
4y is less than or equal to x + 12, -4y is less than or equal to 3x +4, 5x -4y is less than or equal to 4.
A graph of the solution to this system of inequalities on a coordinate plane is shown in the image attached below.
How to graph the solution to this system of inequalities?In order to to graph the solution to the given system of inequalities on a coordinate plane, we would translate the word problem into an algebraic equation and then use an online graphing calculator to plot the given system of inequalities;
4y is less than or equal to x + 12 ⇒ 4y ≤ x + 12.-4y is less than or equal to 3x +4 ⇒ -4y ≤ 3x + 45x - 4y is less than or equal to 4 ⇒ 5x - 4y ≤ 4.Based on the graph (see attachment), we can reasonably infer and logically deduce that the solution to the given system of inequalities is the shaded region as shown in the image attached below.
Read more on inequalities here: brainly.com/question/17064077
#SPJ1
a. glancing through each variable in the products table, which stand out as numerical data, that is, data that would be interesting to add or average? (you may select more than one answer. single click the box with the question mark to produce a check mark for a correct answers and double click the box with the question mark to empty the box for a wrong answers. any boxes left with a question mark will be automatically graded as incorrect.)
The correct answer is Unit Price, Units in Stock, Units on Order, and Reorder Level.
The unit price is the cost of a single item or unit of a product or service. It is usually expressed as a monetary value, such as dollars per item. It can be calculated by dividing the total cost of a product or service by the number of units.
Units in stock refer to the number of items or units of a product or service that are currently available for purchase. It is used to track inventory levels and to manage the replenishment of products or services.
Units on order refer to the number of items or units of a product or service that have been ordered by a company but have not yet been received. It is used to track expected inventory levels and to manage the replenishment of products or services.
The reorder level, also known as the reorder point, is the point at which a company needs to replenish its inventory of a particular product or service. It is determined by calculating the lead time (the time it takes to receive new inventory after placing an order) and the average daily usage of the product or service.
Therefore, The correct answer is Unit Price, Units in Stock, Units on Order, and Reorder Level.
To know more about unit price refer to:
brainly.com/question/10503561
#SPJ4
A family has two cars. The first car has a fuel efficiency of 15 miles per gallon of gas and the second has a fuel efficiency of 30 miles per gallon of gas. During one particular week, the two cars went a combined total of 975 miles, for a total gas consumption of 45 gallons. How many gallons were consumed by each of the two cars that week?
Answer: We can start by using algebra to represent the information given in the problem. Let x be the number of gallons consumed by the first car and y be the number of gallons consumed by the second car.
We know that:
x + y = 45 (the total number of gallons consumed by both cars)
15x + 30y = 975 (the total number of miles driven by both cars, given the fuel efficiency of each car)
We have two equations and two unknowns, so we can use these equations to solve for the value of x and y.
From the first equation, we can solve for x:
x = 45 - y
We can substitute this expression of x into the second equation:
15(45 - y) + 30y = 975
Simplifying the left side of the equation:
675 - 15y + 30y = 975
Subtracting 675 from both sides:
15y = 300
And finally divide both sides by 15:
y = 20
So the second car consumed 20 gallons of gas that week.
We can substitute this value of y back into the equation x = 45 - y to find the value of x
x = 45 - 20 = 25
So the first car consumed 25 gallons of gas that week.
Step-by-step explanation:
Oil is spilled onto a kitchen floor. The area covered by the oil at time t is given by the function A, where A(t) is measured in square centimeters and tis measured in seconds. Which of the following gives the rate at which the area covered by the oil is changing at time t=10? A A(10) B A(11) – A(9) с A(10) 10 A' (10)
The rate at which the area covered by the oil is changing at time t = 10 is A'(10).
Oil is spilled onto a kitchen floor. The function A, where A(t) is measured in square centimeters and t is measured in seconds, gives the area covered by the oil at time t.
Given that the region that was covered in oil at time t = A(t)
We must differentiate A(t) with respect to time t in order to calculate the rate of change in the area covered by the oil over time.
By differentiation:
[tex]\frac{dA}{dt}=A'(t)[/tex]
The rate at which the oily area is transforming is t = 10
[tex]\frac{dA}{dt}|_{t=10}=A'(t)|_{t=10}[/tex]
[tex]\frac{dA}{dt}=A'(10)[/tex]
Hence, the rate at which the area covered by the oil is changing at time t = 10 is A'(10).
To learn more about rate here:
https://brainly.com/question/23634231
#SPJ4
1/5 plus 5/8 is about 3/4 is this reasonable or not
No, Its is not reasonable that 1/5 plus 5/8 is about 3/4.
What is Addition?The process of combining two or more numbers is called the Addition. The 4 main properties of addition are commutative, associative, distributive, and additive identity.
We have to given that;
⇒ 1/5 plus 5/8 is about 3/4
Now, We can add as;
⇒ 1/5 + 5/8
⇒ (8 + 25) / 40
⇒ 33/40
≠ 3/4
Thus, Its is not reasonable that 1/5 plus 5/8 is about 3/4.
Learn more about the addition visit:
https://brainly.com/question/25421984
#SPJ1
in the graph below, what best describes the average acceleration from 40 to 70 s?
The typical increase in speed from 40 to 70 seconds The magnitude is lower than the initial acceleration and is positive.
How do you describe average acceleration?The velocity change's average acceleration is referred to as this. To calculate any object's average acceleration, we divide the change in velocity by the amount of time that has passed. As a result, it is clear that the average acceleration is defined as the ratio of the change in velocity to the change in time over a certain interval.
The average acceleration is the velocity change divided by the time that has passed. A marble's average acceleration is 20 cm/s, for instance, if its velocity increases from 0 to 60 cm/s in three seconds. The marble's speed will increase by 20 cm/s every second as a result. The ball will therefore have an upwards-moving terminal velocity of 20 m/s after two seconds.
To learn more about average acceleration refer to :
https://brainly.com/question/26246639
#SPJ1
Graph a right triangle with the two points forming the hypotenuse. Using the sides, find the distance between the two points in simplest radical form. (3, 2) and (-5, -7)
The distance between the two points in simplest radical form (3, 2) and (-5, -7) is [tex]\sqrt{40}[/tex]
Find the distance?We must determine the hypotenuse's length in order to answer the question because the hypotenuse's endpoints have been provided.
We must determine the hypotenuse's length in order to answer the question because the hypotenuse's endpoints have been provided.
The formula, Distance =, determines the distance between the two positions (x1, y1) (x2, y2).
The formula, Distance =, determines the distance between the two positions (x1, y1) (x2, y2).
Distance = [tex]\sqrt{(x2 - x1)(y2 - y1)}[/tex]
Distance between the two positions (3, 2) and (--5, --7) equals
Distance =root of ( -5 - 3,-7 - 2)
root of (-8 * -5) = [tex]\sqrt{40}[/tex].
To learn more about distance refer to:
https://brainly.com/question/26550516
#SPJ1
I only need questions 7,8,9,10 answered pls
The measure of ∠2 is [tex]54^{0}[/tex], ∠3 is [tex]23^{0}[/tex], ∠6 is [tex]121^{0}[/tex].
Answers to 7, 8, 9, 10:7.- The sum of the internal angles in a triangle equals 180°.
2x + 22 + 4x + 11 + [180- (9x - 15)] = 180
6x + 180 - 9x + 15 = 180 - 33
-2x = 147 - 180 - 15
-2x = -48
x = -48/-3
x = 16
∠X = 2(16) + 22
∠X = 54°
8. 8x - 31 + 6x - 8 + [180 - (10x + 17)] = 180
14x - 39 + 180 - 10x - 17 = 180
4x = 56
x = 56 / 4
x = 14
∠ ECD = 180 - 10(14) - 17
∠ECD = 180 - 140 - 17
∠ECD = 23°
9.- In ΔABC
m ∠C = m ∠A - 9
m ∠B = 4m∠A - 15
The sum of the internal angles in a triangle equals 180°.
∠A + ∠B + ∠C = 180°
∠A + 4∠A - 15 + ∠A - 9 = 180
6∠A = 180 + 24
6∠A = 204
∠A = 204 / 6 = 34
Then, ∠B = 4∠A - 15
∠B = 4(34) - 15
∠B = 121
10.- ∠XYZ = 2∠X - 9
m ∠W = 38°
38 + ∠X + [180 - (2∠X - 9)] = 180
38 + ∠X + 180 - 2∠X + 9 = 180
-1∠X = -47⇒∠X = -47/-1
∠X = 47
Then, ∠XYZ = 2(47) - 9
∠XYZ = 85°
Therefore, the measure of ∠2 is [tex]54^{0}[/tex], ∠3 is [tex]23^{0}[/tex], ∠6 is [tex]121^{0}[/tex] and ∠XYZ is [tex]85^{0}[/tex].
To learn more about sum of the internal angles refers to;
brainly.com/question/13743234
#SPJ1
Suppose P dollars is invested with an annual interest rate of 3.5% compounded semiannually. Use the laws of exponents to find the equivalent annual rate.
Answer:
3.53%
Step-by-step explanation:
annual 3.5%
So half a year =1.75% and compound twice a year.
equivalent annual rate is (1+1.75%)^2 -1 =.0353 =3.53%
let be the linear transformation that first rotates points clockwise through ( radians) and then reflects points through the line . find the standard matrix for .
The formula for the standard matrix for the linear transformation is as follows: beginbmatrix cosfracpi2 & -sinfracpi2 & 0 sinfracpi2 & & cosfracpi2 & 0 & & -1 endbmatrix
The following linear transformation rotates the points by[tex]$fracpi$[/tex]radians in the direction of rotation before reflecting the points through the line. We begin by examining the rotational component of the transformation to determine the standard matrix. A matrix beginbmatrix cosfracpi2 & -sinfracpi2 & 0 sinfracpi2 & cosfracpi2 & 0 0 & 0 & 1 endbmatrixan be used to describe the rotation by radians. We can use the matrix beginbmatrix 1 & 0 & 0 0 & -1 & 0 0 & 0 & 1 endbmatrixfor the reflection component. We obtain the final standard matrix for the linear transformation by multiplying these two matrices. $$beginbmatrix cosfracpi2 & -sinfracpi2 & 0 sinfracpi2 & cosfracpi2 & 0 0.
Learn more about matrix here
https://brainly.com/question/28180105
#SPJ4
The complete question is
let be the linear transformation that first rotates points clockwise through ( radians) and then reflects points through the line . find the standard matrix for the standard matrix of the transformation can be found by first computing the matrix of the rotation and then the matrix of the reflection.
rewrite the (numerical) matrix equation below in symbolic form as a vector equation, using symbols subscript[v, 1], subscript[v, 2], \[ellipsis] for the vectors and subscript[c, 1], subscript[c, 2], \[ellipsis] for scalars. define what each symbol represents, using the data given in the matrix equation.
Given matrix equation as a vector equation:
[tex]\begin{bmatrix}c_1 & c_2 & c_3 & c_4 & c_5\\d_1 & d_2 & d_3 & d_5 & d_5\end{bmatrix}~\begin{bmatrix}v_1\\ v_2\\v_3\\ v_4\\v_5\end{bmatrix}=\begin{bmatrix}8\\-1\end{bmatrix}[/tex]
We know tha a matrix equation is nothing but the equation of the form Av = b,
where A is m × n matrix, ( It is called the coefficient matrix),
v is n × 1 column vector,
and b is m × 1 column vector.
A matrix equation is also called a matrix–vector equation.
Consider given matrix equation.
[tex]\begin{bmatrix}-3 & 5 & -4 & 9 & 7\\5 & 8 & 1 & -2 & -4\end{bmatrix}~\begin{bmatrix}-3\\ 2\\4\\ -1\\2\end{bmatrix}=\begin{bmatrix}8\\-1\end{bmatrix}[/tex]
We need to write the this matrix equation as a vector equation, using symbols v₁, v₂, v₃, . . . for vectors and c₁, c₂ and c₃, . . . for scalars.
We can observe that the first matrix is 2 × 5 matrix and the solution matrix is also 2 × 1
So, it can be rewritten as c₁, c₂, c₃, c₄ and c₅ for the first row and for the second row of matrix d₁, d₂, d₃, d₄ and d₅
Then we multiply those rows with vector v₁, v₂, v₃, v₄ and v₅ we'll get the resultant matrix.
So, we get a vector equation as:
[tex]\begin{bmatrix}c_1 & c_2 & c_3 & c_4 & c_5\\d_1 & d_2 & d_3 & d_5 & d_5\end{bmatrix}~\begin{bmatrix}v_1\\ v_2\\v_3\\ v_4\\v_5\end{bmatrix}=\begin{bmatrix}8\\-1\end{bmatrix}[/tex]
Learn more about the vector equation here:
https://brainly.com/question/29132693
#SPJ4
Find the complete question below.
Assume that for palm oil, groundnut oil and kerosene: 30 mentholatum jars = 1 bottle 24 bottles ≈ 1 tin (a) A tin contains 25 l of groundnut oil. Estimate the capacity, in litres, of a bottle. Estimate the capacity, in ml, of a mentholatum jar. (b) A trader pays #250 for a tin of kerosene and sells it in bottles. If he makes a profit of just over 100 on each tin, estimate the selling price per bottle.
answer4534bottles
Step-by-step explanation:
Two communications companies offer calling plans. With Company X, it costs 30c to connect and then 4c for each minute. With Company Y, it costs 15c to connect and then 3c for each minute. Write and simplify an expression that represents how much more Company X charges, in cents, for n minutes.
The expression that represents how much more Company X charges, in cents, for n minutes is 15 + n
How to write and simplify an expression that represents how much more Company X charges?An algebraic expression is a mathematical phrase that can contain numbers, variables, and operations. It can be used to represent a specific value or a range of values e.g. 2x+3.
For Company X:
Since it costs 30c to connect and then 4c for each minute, we can write the expression as:
30 + 4n
For Company Y:
Since it costs 15c to connect and then 3c for each minute, we can write the expression as:
15 + 3n
An expression that represents how much more Company X charges, in cents, for n minutes is:
(30 + 4n) - (15 + 3n) = 30 - 15 + 4n -3n = 15 + n
Learn more about algebraic expression on:
brainly.com/question/4344214
#SPJ1
Enter the equation for the graph y=[?] cos([?]x)
The equation for the graph will be
[tex]y=1 cos(3x)[/tex]
Define the function y = cos(2x + π/4) ?The function y = cos(2x + π/4) is a cosine function where the independent variable x is multiplied by 2 and then has π/4 added to it before the cosine is applied. The amplitude of this function is 1 and the period is π.
In this question
[tex]we assume, \\y=acos(bx)\\\\when x=0y=1\\\\y=acos(bx)\\\\1=acos0\\\\a=1\\so y=cos(bx)\\\\when x=\pi/3 y=-1\\y=cos(b.\pi/3)\\-1=cos1b.pi/3=cos(pi)\\b=3[/tex]
[tex]y=acosbx[/tex]
[tex]so, y=1.cos(3x)[/tex]
To know more about the cosine function visit:
https://brainly.com/question/17954123
#SPJ1