In finding a number between 9/8 and 10/8, we can use the average of these two.
We can ensure that this number lies between this two.
[tex]Ave=\frac{1}{2}(a+b)[/tex]where a and b are the two numbers
So we have :
[tex]\begin{gathered} Ave=\frac{1}{2}\times(\frac{9}{8}+\frac{10}{8}) \\ =\frac{9}{16}+\frac{10}{16} \\ =\frac{19}{16} \end{gathered}[/tex]Therefore, one number that lies between 9/8 and 10/8 is :
[tex]\begin{gathered} \frac{19}{16} \\ or \\ 1\frac{3}{16} \end{gathered}[/tex]From sin²x + cos²x = 1, prove other two identities
Answer:
[tex]{ \tt{ { \sin}^{2} x + \cos {}^{2}x = 1 }}[/tex]
- Divide through by cos²x ;
[tex]{ \tt{ \frac{ { \sin }^{2}x }{ \cos {}^{2} x} + \frac{ \cos {}^{2} x }{ { \cos }^{2} x} = \frac{1}{ { \cos }^{2}x } }} \\ \\ { \boxed{ \tt{ { \tan}^{2} x + 1 = { \sec }^{2} x}}}[/tex]
- Divide tgrough by sin²x;
[tex]{ \tt{ \frac{ { \sin }^{2}x }{ { \sin}^{2}x } + \frac{ \cos { }^{2}x }{ { \sin}^{2}x } = \frac{1}{ { \sin}^{2} x} }} \\ \\ { \boxed{ \tt{1 + { \cot }^{2}x = \csc {}^{2} x}}}[/tex]
Answer:
See below for proof.
Step-by-step explanation:
Given trigonometric identity:
[tex]\large\boxed{\sin^2x+\cos^2x =1}[/tex]
To prove the identity 1 + cot²x = cosec²x :
[tex]\boxed{\begin{aligned}\sin^2x+\cos^2x &=1\\\textsf{Divide by $\sin^2x$}\implies \dfrac{\sin^2x}{\sin^2x}+\dfrac{\cos^2x}{\sin^2x}& =\dfrac{1}{\sin^2x}\\1+\left(\dfrac{\cos x}{\sin x}\right)^2&=\left(\dfrac{1}{\sin x}\right)^2\\1+(\cot x)^2&=(\text{cosec}\: x)^2\\1+\cot^2x&=\text{cosec}\: ^2x\end{aligned}}[/tex]
To prove the identity tan²x + 1 = sec²x :
[tex]\boxed{\begin{aligned}\sin^2x+\cos^2x &=1\\\textsf{Divide by $\cos^2x$}\implies \dfrac{\sin^2x}{\cos^2x}+\dfrac{\cos^2x}{\cos^2x}& =\dfrac{1}{\cos^2x}\\\left(\dfrac{\sin x}{\cos x}\right)^2+1&=\left(\dfrac{1}{\cos x}\right)^2\\(\tan x)^2+1&=(\sec x)^2\\\tan^2x+1&=\sec ^2x\end{aligned}}[/tex]
Additional identities used:
[tex]\boxed{\begin{minipage}{4 cm}\underline{Trigonometric Identities}\\\\$\tan \theta=\dfrac{\sin \theta}{\cos \theta}$\\\\$\cot \theta=\dfrac{\cos \theta}{\sin \theta}$\\\\$\csc \theta=\dfrac{1}{\sin \theta}$\\\\$\sec \theta=\dfrac{1}{\cos \theta}$\\\end{minipage}}[/tex]
6. This number is the same as sixty-eight and 830 thousandths.
The most appropriate choice for decimal will be given by-
The number is 68.830
What is decimal?
The type of numbers which has a whole number part and a fractional part and the whole number part is seperated from the fractional part by a decimal point is known as decimal.
Decimal can be terminating as well as non terminating
Terminating decimal numbers are those numbers which has finite number of figures after the decimal point.
Non terminating decimal numbers are those numbers which has infinite number of figures after decimal points.
Here,
The required number is the same as sixty-eight and 830 thousandths.
So, the number is 68.830
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Find the midpoint of the line segment joining the points (7,6) and (-3,- 6).
The provided line segment's midpoint is (x, y) =. (2, 0)
What is the midpoint?The midpoint of a line segment is referred to as the midpoint in mathematics. The third side of a triangle is parallel to the segment when two line segments of a triangle are joined. It is the average value of the coordinates' endpoints.
The provided coordinates for the line segment, according to the query, are: (7, 6) and (-3, -6).
The line segment's midpoint can be determined using the following formula:
Midpoints = [tex]\frac{x1+x2}{2} ; \frac{y1+y2}{2}[/tex]
And the values for calculating the midpoint are as follows: x1 = 7, x2 = 3, y1 = 6, y2 = -6.
When we enter these values into the formula, we obtain
Midpoint (x, y): (7 + (-3), 6 + (-6)
Mid point (x, y) equals 2 and 0
Hence, the halfway point for the given line segment is: (x, y) = (2, 0).
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Two angles are supplementary . One angle is 5 less than four times the other . Find the measures of the angles let x equal the first angle.let y equal the second angle
Statement Problem: Two angles are supplementary . One angle is 5 less than four times the other . Find the measures of the angles
olution:
Circle the whole numbers and explain the reasoning : 9, 4/4, and 1.00000
Answer:
9, 4/4, and 1.00000
Explanation:
Whole numbers are the basic counting numbers 0,1,2,3,4,...There is no fractional or decimal part. And no negatives.
Given the numbers:
• Firstly, 9 is clearly a whole number
,• 4/4 = 1. 4/4 is a fraction that is equivalent to a whole number. Therefore, it is a whole number.
,• 1.00000=1. Whenever there is a decimal in which all the digits after the decimal point are zeros, the number is a whole number.
K
Suppose that a certain car has the following average operating and ownership costs.
Average Costs per Mile
Operating
$0.28
Ownership
50.74
a. If you drive 30,000 miles per year, what is total annual expense for this car?
b. If the total annual expense for this car is deposited at the end of each year into an IRA paying 8.5% compounded
nt
[(¹)
yearly, how much will be saved at the end of nine years? Use the formula A=
a. If you drive 30,000 miles per year, the total annual expense for this car is $ 30,600
(Round to the nearest dollar as needed.)
1
k
b. If the total annual expense for this car is deposited at the end of each year into an IRA paying 8.5% compounded
yearly, the amount saved at the end of nine years is $
(Round to the nearest dollar as needed.)
S
LIC
(0,0)
Total
$1.02
More
x
rrect: 1
Total annual expense= $8400
Saving= $622,834,634,198.44
What is compound interest?Compound interest is addition of interest to the principal sum of a loan or deposit, or in other words, interest on principal plus interest. It is result of reinvesting interest, or adding it to the loaned capital rather than paying it out, or requiring payment from borrower, so that interest in the next period is then earned on principal sum plus previously accumulated interest. Compound interest is standard in finance and the economics.
Compound interest is contrasted with the simple interest, where previously accumulated interest is not added to the principal amount of the current period, so there is no compounding. The simple annual interest rate is interest amount per period, multiplied by the number of periods per year. The simple annual interest rate is also known as nominal interest rate (not to be confused with the interest rate not adjusted for inflation, which goes by the same name).
a)Total annual expense= total miles *average cost per mile
= 30,000* 0.28= $8400
b)Amount deposited in 9 years= 8400*9= $75,600
total amount after 9 years= FV= PM[tex][(1+r)^{n}-1]/r[/tex]
=8400* [tex][(1+8.5)^{9}-1]/8.5[/tex]
=$622,834,709,798.44
Savings=622,834,709,798.44 -75600= $622,834,634,198.44
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What is the lowest value of the range of the function shown on the graph? A. - ∞B. - 2C. 0D. 3
-2
Explanations:The range of the function is a set of all the values of y on the graph
The lowest point of the graph on the y-axis is -2
Therefore, the lowest value of the range of the function shown on the graph is -2
I need help with this problem
We have,
[tex]\begin{gathered} e^{\ln x}=x \\ \log _ex=\ln x \end{gathered}[/tex]The given expression is,
[tex]\ln 5x=4[/tex]This can be written as,
[tex]\begin{gathered} \ln 5x=4 \\ \log _e5x=4 \\ e^4=5x \end{gathered}[/tex]A standard die is rolled. Find the probability that the number rolled is odd.
Answer
Explanation
To determine the probability that the number rolled is odd using a standard die, we first list the total outcomes as shown below:
1,2,3,4,5,6
As we can see, the odd numbers are:
1,3,5
This means that the total favorable outcomes is 3.
Now, we use the formula:
[tex]Probability=\frac{favorable\text{ outcomes}}{Total\text{ outcomes}}[/tex]We plug in what we know:
[tex]\begin{gathered} Probab\imaginaryI l\imaginaryI ty=\frac{favorable\text{ outcomes}}{Total\text{ outcomes}} \\ =\frac{3}{6} \\ Simplify \\ Probab\mathrm{i}l\mathrm{i}ty=\frac{1}{2} \end{gathered}[/tex]Therefore, the probability that the number rolled is odd is 1/2.
Answer:
3/6
A standard die has 6 sides, numbered 1 through 6 (1,2,3,4,5,6). That means we have 3 odd numbers (1,3,5) and 3 even numbers (2,4,6).
The total possible outcomes of an odd number are 3, because there are 3 odd numbers, and the total outcomes are 6. So we write it as 3/6, like 3 out of six chances of getting an odd number.
It can be simplified to 1/2.
hope it helps, mark as brainliest :D
pls help me with math i’ll give you brainlist
Answer:
8
Step-by-step explanation:
8+8=16 see i helped u GIVE ME BRAINLIST NOW PLSS I BEG :.)
A retailer is looking to evaluate its customer service. Management has determined that if the retailer wants to stay competitive, then it will have to have at least a 90% satisfaction rate among its customers. Management will take corrective actions if the satisfaction rate falls below 90%. A survey of 1,200 customers showed that 1,068 were satisfied with their customer service.
Answer:
They have an 89% satisfaction rate, less than the goal.
Step-by-step explanation:
To find this, divide 1068/1200, this gives you 0.89
This shows that they have an 89% satisfaction rate.
Since, the satisfaction rate 89% which is less than 90%. Therefore, management will take corrective actions.
Given that, if the retailer wants to stay competitive, then it will have to have at least a 90% satisfaction rate among its customers.
What is percentage?Percentage is defined as a given part or amount in every hundred. It is a fraction with 100 as the denominator and is represented by the symbol "%".
A survey of 1,200 customers showed that 1,068 were satisfied with their customer service.
Here, the satisfaction rate = 1068/1200 ×100
= 0.89 ×100
= 89%
Since, the satisfaction rate 89% which is less than 90%. Therefore, management will take corrective actions.
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1. The amount of time 26 students spend on their phones on a given day (rounded to the nearest
hour) is recorded as follows.
0, 3, 4, 4, 5, 5, 6, 6, 6, 7, 7, 7, 7, 8, 8, 8, 8, 9, 9, 9, 10, 10, 10, 11, 11, 12
Create a dot plot of the information. *Be sure to label all necessary parts!
The amount of time 26 students spend on their phones represent by a dot plot:
take the smallest and highest data from the given record. i.e., 0 and 12.As the data given is: 0(1 time), 3(1 time), 4,4(2 times), 5,5(2 times), 6,6,6(3 times), 7,7,7,7(4 times), 8,8,8,8(4 times), 9,9,9(3 times), 10,10,10(3 times), 11,11(2 times) and 12(1 time) occurrence.divide the whole line between 0 to 12 representing the number of hours spent.start dotting out points with their respective data with the number of times one above another( if data is more than one)To learn more about dot plots, follow the below link:
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Answer:
See attachment.
Step-by-step explanation:
A Dot Plot is a graphical display of quantitative data consisting of dots plotted on a simple scale.
If a value occurs more than once, the dots are placed one above the other so that the height of the column of dots represents the frequency for that value.
Given data set:
{0, 3, 4, 4, 5, 5, 6, 6, 6, 7, 7, 7, 7, 8, 8, 8, 8, 9, 9, 9, 10, 10, 10, 11, 11, 12}
Step 1Label the increments on the given line to include the range of data.
Label them -2 to 16 increasing in 1 unit.
Step 2Label the dot plot with a suitable title describing what the dot plot represents.
Place "Time students spent on their phones on one given day (nearest hour)" under the line.
Step 3Count the number of data points for each discrete category:
[tex]\begin{array}{|c|c|}\cline{1-2} \sf Category & \sf Frequency\\\cline{1-2} 0 & 1\\\cline{1-2} 3 & 1\\\cline{1-2} 4 & 2\\\cline{1-2} 5 & 2\\\cline{1-2} 6 & 3\\\cline{1-2} 7 & 4 \\\cline{1-2} 8 & 4 \\\cline{1-2} 9 & 3\\\cline{1-2} 10 & 3\\\cline{1-2} 11 & 2\\\cline{1-2}12 & 1\\\cline{1-2}\end{array}[/tex]
Draw a stack of dots that number high for each category.
(See attachment).
Solve the equation. e – 36 = 133 A. e=97 B. e=107 C. e= 169 D. e=179
Answer:
d
Step-by-step explanation:
Write the scale factor
Let:
[tex]\begin{gathered} FO\cdot k=QK \\ \end{gathered}[/tex]Where:
k = scale factor
so:
[tex]\begin{gathered} 18k=24 \\ k=\frac{24}{18} \\ k=\frac{4}{3} \end{gathered}[/tex]now, we can find y and x:
[tex]\begin{gathered} \frac{4}{3}\cdot x=28 \\ x=\frac{28\cdot3}{4} \\ x=21 \end{gathered}[/tex][tex]\begin{gathered} 15\cdot\frac{4}{3}=y \\ 20=y \end{gathered}[/tex]what does 2056x18394= / anyone up to ta lk
The product of the multiplication of (2056 * 18394) is 37818064.
As per the question statement, we are provided with the multiplicative statement of two numbers, 2056 and 18394.
We are required to perform the above mentioned multiplication and determine the product in the simplified form a number.
To solve this question, we simply need to multiply 2056 and 18394, and mention the upcoming product as our required answer, i.e.,
(2056 * 18394) = 37818064.
Hence, The product of the multiplication of (2056 * 18394) is 37818064.
Multiplication: In Mathematics, Multiplication is one of the four basic arithmetic operations, alongside addition, subtraction, and division which means the repeated addition of groups of equal sizes. Product: In mathematics, a product is the result of a multiplication, or an expression that identifies two or more factors or numbers of decimals to be multiplied.To learn more about Multiplication & Products, click on the link below.
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A jet engine close up produces sound at 152 decibels. What is the decibel reading of a pair of nearby jet engines? (Round your answer to the nearest decibel.)
If a jet engine close up produces sound at 152 decibels then the decibel reading of a pair of nearby jet engines is 168.62 decibel
A jet engine close up produces sound at 152 decibels
The the relative intensity of one jet engine = [tex]126^{152}[/tex]
The relative intensity of a pair of jet engines = 2× [tex]126^{152}[/tex]
The reading of a pair of nearby jet engine in decibel = 10log(The relative intensity of a pair of jet engines)
Substitute the values in equation
The reading of a pair of nearby jet engine in decibel = 10×log(2× [tex]126^{152}[/tex])
= 168.62 decibel
Hence, if a jet engine close up produces sound at 152 decibels then the decibel reading of a pair of nearby jet engines is 168.62 decibel
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A player tosses a fair coin n times. Each time, if the coin lands on Head, the player
win a dollar, otherwise, the player loses a dollar. What is the expected earning of the
player? What is the variance of the earning of the player? Now the player apply a
new strategy: the player will play the game until he gets a head. What is the expected
earning of the new strategy? Does the result depend on n?
Noah invested $2500 in an account paying 3% simple interest. What was the total
amount in his account after 5 years?
Answer:
$2,875
Step-by-step explanation:
Interest = Principal x rate x time
Interest = $2500 x 0.03 x 5
Interest = $375
Original value + interest = Total amount
$2,500 + $375 = $2,875
2. The sprinklers run 5 hours each day. The monthly (30 days) water bill is $500. How much
does it cost to run the sprinklers for an hour? Round your answer to the nearest cent.
6RI2
Answer:
$3.33 (rounded) per hour
Step-by-step explanation:
The sprinklers run 5 hours each day. The monthly (30 days) water bill is $500. How much does it cost to run the sprinklers for an hour? Round your answer to the nearest cent.
hours run per month = daily hours × days in month
hours run per month = 5 × 30
hours run per month = 150
if the total bill was $500 for 150 hours then:
$500 ÷ 150 = $3.33 (rounded) per hour.
Which of the following is true?
C
70°
1/2
B
D
130°
A. m<BCD - m<DBC = 10°
B. m<BCD - m<DBC = 20°
C. m<BCD - m<DBC = 60°. D. m<BCD m<DBC = 80°
The correct answer is [a] m<BCD - m<DBC =10°
An angle is a figure in Euclidean geometry made up of two rays that share a common terminal and are referred to as the angle's sides and vertices, respectively.
What is an angle?An angle is a figure in Euclidean geometry made up of two rays that share a common terminal and are referred to as the angle's sides and vertices, respectively. Angles created by two rays are in the plane where the rays are located. The meeting of two planes also creates angles. We refer to these as dihedral angles. The angle formed by the rays lying perpendicular to the two crossing curves at the point of junction is another property of intersecting curves.
Angle can also refer to the length of a rotation or an angle. This metric represents the relationship between a circular arc's length and radius. The arc is centered at the vertex and defined by the sides in the case of a geometric angle. When there is a rotation, the arc is defined by any other point and the rotation's image, and it is centered at the rotation's center.
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What is the answer do this please
Answer:
r = 5%
Step-by-step explanation:
Formula : I=PRT
GIVEN:
I = 125
P = 5000
R = R
T = 6
125= (5000)(R)(0.5)
125=2500R
0.05=R
Interest rate = 0.05(100)
= 5%
Stacia needs 39 bulbs for every 3 chandeliers she makes.
Complete the table using equivalent ratios.
13 diamonds, y = 3 chandeliers, x = 52 diamonds, x = 130 diamonds, y = 40 chandeliers. this is the complete table using equivalent ratios.
What is equivalent ratio?When we compare any two kinds of ratios, they are said to be equivalent. To determine whether these two or more ratios are equivalent, they can also be compared to one another. For instance, the ratios 1:2 and 2:4 can be called as equivalent.
Describe ratioSimply put, a ratio is a comparison of two numbers. When a ratio is equal, the proportionate relationship remains constant. By multiplying the first value by the same ratio, or unit of proportion, you can determine your own equivalent ratios.
Which ratio is equivalent?It is possible to treat an equivalent ratio and a proportion interchangeably. An equivalent ratio is the result of simplifying the two ratios to the same fraction.
Let us take the value of x -----> the number of diamonds
Let us take the value of y ----> the number of chandeliers
we know that
The ratio present between the number of diamonds to that of the number of chandeliers is equal to
[tex]\frac{x}{y} = \frac{39}{3}[/tex]
1) for y = 1,
x = 13 diamonds
2) for x = 39
y = 3 chandeliers
3) for y = 4
x = 52 diamonds
4) y = 10
x = 130 diamonds
5) x = 520
y = 40 chandeliers
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Answer: 52 and 130
Step-by-step explanation:
Before art class starts, Gordon makes sure that each table has a full bowl of paint. He has 1/2 of gallon of paint and it able to fill the bowls for all 7 tables. How many gallons of paint does each table have?
Based on the fact that Gordon has 1/2 gallons of paint and is able to fill up bowls in 7 tables, the number of gallons of paint each table has is 1/14 gallons of paint
How to find the number of gallons?Gordon has 1/2 gallons of paint and knows that this amount of paint can given each bowl in all 7 tables, a full bowl of paint.
The amount of paint that each bowl gets can therefore be calculated by the formula:
= Gallons of paint Gordon has / Number of tables
Solving for the paint each bowl has gives:
= 1/2 ÷ 7
= 1/2 x 1/7
= 1/14 gallons of paint
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What is f(g(13))?
A mapping diagram is shown.
Answer:
(c) 32
Step-by-step explanation:
Given a map between x, g(x), and f(g(x)), you want to find f(g(13)).
Using a mapYou want the function value that results when 13 is the argument of g(x), and g(x) is the argument of f(x).
Locate the input (13) in the left column of the diagram. Follow the arrow to find g(13) = 16. Follow the arrow again to find f(16) = 32.
f(g(13)) = 32
By applying the elimination method, solve the following pair of simultaneous equations:
− 2 = 4
4 + 2 = 6
By applying the elimination method the value of x is - 2 and y is 7.
This is a problem from algebraic equations and we have to apply the elimination method. We can solve this problem by following a few steps.
So, the given equation according to the question is,
− 2x = 4 ................ ( equation 1 )
4x + 2y = 6 ............... ( equation 2 )
While applying the elimination method we have to multiply equation (1) with the positive coefficient of x in the second equation and vice versa.
Here the coefficient of x in the first equation is 2 and in the second equation is 4.
Now, we have to multiply equation ( 1 ) with 4 and equation ( 2 ) with 2.
Therefore,
− 2x = 4 ................ ( equation 1 ) × 4
4x + 2y = 6 ............... ( equation 2 ) × 2
Now, we can rewrite the equations as,
− 8x = 16 .................. ( equation 3 )
8x + 4y = 12 .................. ( equation 4 )
Now the coefficient of x in both equations are same but opposite sign. So, we have to add the equations.
Here we get , -8x + 8x + 4y = 16 + 12
Or, 4y = 28
Or, y = 7
Now, we have to put the value of y in any equation.
4x + 2.7 = 6 ( equation 2 )
Or, 4x = 6 - 14 = -8
Or, x = -2
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The correct question :
By applying the elimination method, solve the following pair of simultaneous equations:
− 2x = 4
4x + 2y = 6
the ______ is a point at which three or more lines intersect OPTIONS;A.median B.angleC.point of concurrencyD.perpendicular bisector
ANSWER:
C. point of concurrency
STEP-BY-STEP EXPLANATION:
The only point where these lines cross each other is called the point of concurrency.
Therefore:
The point of concurrency is a point at which three or more lines intersect.
The correct answer then is C. point of concurrency
Micaela is working two summer jobs, making $13 per hour tutoring and making $10
per hour landscaping. In a given week, she can work at most 13 total hours and must
earn a minimum of $140. If a represents the number of hours tutoring and y
represents the number of hours landscaping, write and solve a system of inequalities
graphically and determine one possible solution.
The equations will be a+ y ≤ 13, since Micaela can't work more than 13 hours and also she needs to earn at least $140 each week, so other equation will be 13a + 10y ≥ 140.
What is inequalities?Inequality, a declaration of an order relationship between two numbers or algebraic expressions, such as greater than, greater than or equal to, less than, or less than or equal to.
a = number of hours spent tutoring
y = number of hours spent landscaping
Micaela can't work more than 13 hours, so a + y ≤ 13.
Also, she needs to earn at least $140 each week, so 13a + 10y ≥ 140.
Using intercepts, you may graph things in this format on paper. They must be transformed into slope-intercept form in order to be graphed on a standard graphing calculator.
For instance, if a = 12 and y = 2, then a + y = 13 hours, and 12(13) + 2(10) = $176. Micaela puts in her maximum number of hours and earns more than she should.
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could you answer my question? thanks
a = 252, x = 7; y = 5925.13
Equation is given by the formula:
[tex]y\text{ = y}_0\cdot(1+r)^{^x}{}[/tex]where:
yo = the initial population; r = growth rate, x = time
In your case, yo = 252. And the grow rate is 57%, therefore the r = 0.57. Finally, the exponential equation has this form:
[tex]y\text{ = 252}\cdot1.57^x[/tex]Then, if we want to know what is the population after 7 days, we can evaluate this function:
[tex]y\text{ \lparen7\rparen = 252}\cdot1.57^7\text{ =5925.13}[/tex]When the plumber comes to my house to fix the leaky faucet, he charges a flat rate of $50 in addition to charging $22 per hour. If the final bill was $116, how long was the plumber at my house?
Written as a simplified polynomial in standard form, what is the result when (x+7)^2 is subtracted from7
7-(x^2+14x+49)
7-x^2-14x-49
-x^2-14x-42