9.7 to one significant figure is 10
How to approximate the number?We have:
9.7
To approximate to one significant figure, we have to estimate the number such that it is represented by a non zero digit.
When 9.7 is approximated, we have:
10
Hence, 9.7 to one significant figure is 10
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Katie divided a drink with a volume
of 3½ cups into ½ cup servings.
How many servings did she have?
Answer:
Step-by-step explanation:
she has 7 servings. Add 1/2 + 1/2 until you get 3 1/2 and it equals 7
In a board game, you gain 1.5x the number of coins in your purse every time you pass start. However, you max out at 300 coins. If you have 5 coins in your purse, how many times must you pass until you reach maximum?
Answer:
6
Step-by-step explanation:
The requried number of passes to reach the maximum is given as 10 passes.
What is an exponential function?The function which is in format f(x) =aˣ where a is constant and x is variable, the domain of this exponential function lies (-∞, ∞).
Here,
We have 5 coins in your purse,
We Gain 1.5x the number of coins in your purse every time you pass the start. The maximum number of coins is 300.
According to the quesiton,
5 . 1.5ˣ = 300
Where x is the number of passes,
1.5ˣ = 60
x ≈ 10
Thus, the requried number of passes to reach the maximum is given as 10 passes.
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42+48/6=?
48/6 meaning a fraction not division
Answer:
50
Step-by-step explanation:
Fractions are division problems. :) You have to complete that first to solve the equation (PEMDAS).
48/6 = 8
42 + 8 = 50
which relation describes the graph?
Answer:
A.
Step-by-step explanation:
The other graphs answers have a point at (3, 1) which is not on the graph.
Solve for x in the triangle. Round your answer to the nearest tenth.
14
x
68
X
Answer:
x=15.1
Step-by-step explanation:
Side definitionsIn a right triangle, the side across from the right angle is always the hypotenuse.
The other two sides are termed "legs".
Once one of the other two angles is chosen as the angle to work from, then the two legs can be defined as the "opposite" and the "adjacent"
The leg touching the angle is the "adjacent" leg (or adjacent side), and the leg across from the angle is the "opposite" leg (or opposite side).
Trigonometric function definitions[tex]\sin(\theta)=\dfrac{\text{opposite side}}{\text{hypotenuse}}[/tex]
[tex]\cos(\theta)=\dfrac{\text{adjacent side}}{\text{hypotenuse}}[/tex]
[tex]\tan(\theta)=\dfrac{\text{opposite side}}{\text{adjacent side}}[/tex]
In this situation, the given angle is in the bottom right. A value is given for the side opposite the given angle, and the requested value is on the hypotenuse.
So, the two sides of interest are the "opposite" and the "hypotenuse". The trigonometric function that relates these two sides is the sine function.
Calculating x[tex]\sin(\theta)=\dfrac{\text{opposite side}}{\text{hypotenuse}}[/tex]
[tex]\sin(68^o)=\dfrac{(14)}{(x)}[/tex]
Evaluating the sine function in a calculator (in degree mode):
[tex]0.9271838546...=\dfrac{14}{x}[/tex]
Multiply both sides by x:
[tex](0.9271838546...)x=\left (\dfrac{14}{x} \right)x[/tex]
[tex](0.9271838546...)x=14[/tex]
Divide both sides by the decimal number:
[tex]\left (\dfrac{(0.9271838546...)x}{0.9271838546...} \right)=\dfrac{14}{0.9271838546...}[/tex]
[tex]x=15.0994864...[/tex]
Rounded to the nearest tenth, x=15.1
Find two functions f(x) and g(x) such that h(x) = ( f∘ g)(x) , if h(x) = √ + 5
f(x) = ____________________
g(x) = ____________________
If we know that h(x) = (f ° g) (x) = √x + 5, then f(x) = x + 5 and g(x) = √x by applying the binary operation of composition between two functions.
How to find the two functions behind a composed function
Let be f and g two functions, h is a composition of f with respect to g when the input variable of f is equal to g. The composed function is h(x) = √x + 5 and there may be more than a solution. One of these solutions are f(x) = x + 5 and g(x) = √x.
If we know that h(x) = (f ° g) (x) = √x + 5, then f(x) = x + 5 and g(x) = √x by applying the binary operation of composition between two functions.
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Pls help why did she flip the sign i dont understand
Answer:
See below
Step-by-step explanation:
When you multiply or divide both sides of an inquality equation by a NEGATIVE number , it reverses the symbol to see this in action:
- 4n >36 Instead of dividing by -4 let's ADD - 4n to both sides
0 > 36 + 4n now SUBTRACT 36 from both sides
-36 > 4n re-arrange just a little
4n < -36 <======== see how the symbol has reversed ???
n < -9
Hii!
___________________________________________________________
Answer:
'Cause both sides were divided by a negative number! ^^
Step-by-step explanation:
The sign of the inequality was flipped because you divided both sides of the inequality by -4, which is a negative number.
When we divide, or multiply, both sides of an inequality by a negative number, we flip the inequality sign.
--
Hope that this helped! Best wishes.
--
Genesis throws a ball up in the air. The graph below shows the height of the ball hh in meters after tt seconds. Find the interval for which the ball’s height is decreasing.
help please
We conclude that the interval in which the function decreases is (1.5, 3]
In which interval is the ball's height decreasing?
The ball is decreasing when the graph, reading from left to right, is going downwards.
Particularly, in this parabola that opens downwards, the graph will decrease after the vertex.
And we can see that the vertex is at x = 1.5
And we also see that the graph of the function ends at x = 3.
Then we conclude that the interval in which the function decreases is (1.5, 3]
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Which is the graph of 2x - 4y > 6?
-4 -2
2
-2
2
RUTA
4-2
414
2
O
W
4 -4-2
414
2
-2
O
2
RY
4
-2
2
211
Answer:
(d) see attached
Step-by-step explanation:
There are a couple of quick checks you can do to identify the correct graph.
__
shading and line styleFind a variable with a positive coefficient, and write that in the given relation to the inequality symbol:
x >
This tells you ...
shading is to the right of the line (where x-values are greater)the line is dashed (the = case is not included)location of the lineThe x-coefficient is a factor of the constant, so the x-intercept of the boundary line is easily found. Set y=0, and you have ...
2x = 6
x = 3
The boundary line you're looking for has an x-intercept at x=3.
__
The correct graph is shown in the attachment.
Denise and Stacey went to a carnival. The admission fee was $6 per person. Each ride at the carnival costs c dollars. The game booths charged g dollars for each game. Both Denise and Stacey went on 7 rides each. Stacey played 3 games, while Denise played 2 games. Which expression represents the total amount of money that Denise and Stacey spent at the carnival?
The total amount of money that Denise and Stacey spent at the carnival is 12 + 14c + 5g dollars.
What is total amount?
The amount that you get when you add several numbers or things together.
The total amount of money that Denise and Stacey spent at the carnival will be money spent on admission + ride + game.
Total amount = 2 * 6 + 2 ( 7 * c ) + ( 3 * g + 2 * g )
= 2 * 6 + 14 * c + 5 * g
= 12 + 14c + 5g dollars.
Therefore, the total amount of money that Denise and Stacey spent at the carnival is 12 + 14c + 5g dollars.
The questions seems incomplete, its option could be:
12 + 14c + 5g 12 + 14g + 5c 12 + 7g + 5c 12 + 7c + 5g.
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Tim earns 96pounds for 16 hours. Tim earns 'time and a half' for overtime. he works 4 hours of overtime in addition to his normal 16 hours. how much does he earn altogether
find hourly rate:
96 / 16 = 6 pounds per hour
6 x 1.5 = 9 pounds per hour for overtime.
9 x 4 = 36 pounds
96 + 36 = 132 pounds total
Question 2 of 11
What system of equations would you use to solve the problem below?
A test is worth 100 points. Multiple-choice questions are worth 3 points and
short-answer questions are worth 5 points. If the test has 28 questions, how
many multiple-choice questions are there?
If the number of multiple-choice questions is x and the number of short answer questions is y, then:
[tex]x+y=28\\\\3x+5y=100[/tex]
If f(n)= n²-n, then f(-4) is
O-20
12
-12
20
Answer: 20
Step-by-step explanation:
f(-4) = -4² - (-4)
f(-4) = 16 + 4
f(-4) = 20
You toss a coin and roll a number cube. The table shows the sample space,
where H means heads, T means tails, and the numbers represent the number
cube roll.
H
T
1
H1
T1
2
H2
T2
3
H3
T3
4
H4
T4
5
H5
T5
6
H6
T6
What is the probability of tossing heads and rolling a number less than 3?
Probability helps us to know the chances of an event occurring. The probability of tossing heads and rolling a number less than 3 is 1/6.
What is Probability?Probability helps us to know the chances of an event occurring.
[tex]\rm Probability=\dfrac{Desired\ Outcomes}{Total\ Number\ of\ outcomes\ possible}[/tex]
The number of cases where coins land on heads and a number less than 3 are rolled is 2, which are H1 and H2.
The probability of tossing heads and rolling a number less than 3 is,
Probability = (Outcomes where coins land on heads and a number less than 3 are rolled)/(Total number of cases)
Probability = 2/12 = 1/6
Hence, the probability of tossing heads and rolling a number less than 3 is 1/6.
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Christina knits a scarf for each of her 7 friends. Altogether, the scarfs had a total length of 39.9 ft. if each scarf has the same length. how long was each scarf? write answer in inches
The length of each scarf knitted for the 7 friends given the total length of the scarf altogether is 5.7 ft
Length of each scarfNumber of friends = 7Total length of scarf = 39.9 ftLength of each scarf = Total length of scarf / Number of friends
= 39.9 ft / 7
= 5.7 ft
Therefore, the length of each scarf knitted for the 7 friends given the total length of the scarf altogether is 5.7 ft
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What is the solution to this equation? 2ln4+lnx=3ln2+ln(x+1)
Answer:
[tex]x=1[/tex]
Step-by-step explanation:
Given equation:
[tex]2 \ln 4+\ln x=3 \ln 2+\ln(x+1)[/tex]
[tex]\textsf{Apply the power law}: \quad n \ln x = \ln x^n[/tex]
[tex]\implies \ln 4^2+\ln x=\ln 2^3+\ln(x+1)[/tex]
Simplify:
[tex]\implies \ln 16+\ln x=\ln 8+\ln(x+1)[/tex]
Subtract ln 8 from both sides:
[tex]\implies \ln 16+\ln x- \ln 8=\ln(x+1)[/tex]
Subtract ln x from both sides:
[tex]\implies \ln 16-\ln 8=\ln(x+1)-\ln x[/tex]
[tex]\textsf{Apply the quotient law}: \quad \ln x - \ln y = \ln \frac{x}{y}[/tex]
[tex]\implies \ln \left\dfrac{16}{8}\right = \ln \left(\dfrac{x+1}{x}\right)[/tex]
Simplify:
[tex]\implies \ln 2 = \ln \left(\dfrac{x+1}{x}\right)[/tex]
[tex]\textsf{Apply the equality law}: \quad \textsf{if }\: \ln x= \ln y\:\textsf{ then }\:x=y[/tex]
[tex]\implies 2=\dfrac{x+1}{x}[/tex]
Multiply both sides by x:
[tex]\implies 2x=x+1[/tex]
Subtract x from both sides:
[tex]\implies x=1[/tex]
I need helpppppp asap
Answer:
graph A
Step-by-step explanation:
When looking at a graph, there are two different axes. The vertical values--marked by the center up/down line--are "y-values"; and this is called the "y-axis"
The horizontal values--marked by the left/right line--are "x-values"; and this is called the "x-axis"
For the x-axis, values to the left side of the origin (the place where the y-axis and x-axis intercept) are smaller than 0--they are all negative values.
Values to the right side of the origin are positive--greater than 0.
For the y-axis, positive numbers are on the top half [once again, the midpoint / 0 is where the two lines are both = to 0; the origin] and negative numbers are on the bottom half.
Ordered pairs (points) are written as (x,y)
(x-value, y-value)
We are looking for a graph that decreases (along the y-axis), hits a point below the origin, and goes flat/stays constant.
When a graph is decreasing (note: we read graphs from left to right), the line of the graph is slanted downwards (it looks like a line going down).
So, if we look at the graphs, we can see Graph A descending, crossing the y-axis {crossing the middle line /vertical line / y-axis} at a value of -7, and then staying constant (it is no longer increasing or decreasing because the y-values stay the same)
hope this helps!!
A clothing manufacturer produces one type of sweater that earns $4 profit for each one sold. The business manager requires that a profit of at least $100 be earned every hour. The product manager estimates that the expenses for running the machine are $45 per hour. What is the least number of sweaters that must be produced each hour to earn a profit of at least $100?
The least number of sweaters that must be produced each hour to earn a profit of at least $100 is 37.
What is inequality?It is defined as the expression in mathematics in which both sides are not equal they have mathematical signs either less than or greater than known as inequality.
We have:
A clothing manufacturer produces one type of sweater that earns $4 profit for each one sold.
Let x be the number of sweaters that must be produced each hour to earn a profit of at least $100
Total selling price if earns $4 profit for each one sold = 4x
The expenses for running the machine are $45 per hour.
4x - 45 ≤ 100
4x ≤ 145
x ≤ 145/4
x ≤ 36.25
Number of sweater(estimate value) = 37
Thus, the least number of sweaters that must be produced each hour to earn a profit of at least $100 is 37.
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find the x intercepts of the following linear function 3x-5y=-15
Answer:
(-5, 0)
Step-by-step explanation:
The y value of an x intercept is always 0. Therefore, we can substitute 0 for y in the equation to find the x intercept:
3x - 5(0) = -15
3x = -15
x = -5
The x intercept is (-5, 0)
Briana monitors the number of E. coli infections reported in a certain
neighborhood in a given week. The recent numbers are shown in
this table:
According to her reports, the reported infections are growing at a
rate of 50%.
If the number of infections continues to grow exponentially,what
will the number of infections be in week 6?
An equation is formed of two equal expressions. The number of infections in 6 weeks is 456.
What is an equation?An equation is formed when two equal expressions are equated together with the help of an equal sign '='.
The general equation of an exponential function is written as,
y = A(B)ˣ
Since the infection is increasing at a rate of 50%, therefore, the rate of growth will be,
B = 1.50
Substitute any value then we will get,
40 = A(1.50)⁰
A = 40
Thus, the exponential equation of the growth will be,
y = 40(1.50)ˣ
Now, the number of infections in 6 weeks will be,
y = 40(1.50)⁶
y = 455.625 ≈ 456
Hence, the number of infections in 6 weeks is 456.
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pls someone help me asap
Answer:
Area: 15.53 square inches
Perimeter: 15.71 inches
Step-by-step explanation:
Area:
So the area of the rectangle is pretty easy to find and is just the width * height. In this case it's 4 * 3 which is 12. Now the area of a circle is [tex]\pi r^2[/tex]. But since this is a semi circle it's half of that which is [tex]\frac{\pi r^2}{2}[/tex]. The diameter of the semicircle is 3 as it sits on top of the rectangle. The radius is half of the diameter so the radius is 1.5. Now plug that into the equation and you get [tex]\frac{(3.14) (1.5)^2}{2} = 3.5325[/tex]. Now add that to 12 and you get 15.5325. Round that number to the nearest hundredth and you get 15.53. So that's the area.
Perimeter:
Pi is the ratio of any circle's circumference to the diameter. Or in other words the circumference is equal to the diameter * 3.14. The diameter is 3 which you multiply by 3.14 to get the circumference of a circle. This will get you 9.42 but since it's a semicircle, the circumference is half of this value which is 4.71. The perimeter of the rectangle is just 2 times the width + 2 times the height. This is not completely the case in this shape since one of the sides of the rectangle is not a side of the two shapes joined together. Which is the side that is parallel to the side of length 3 inches. So the perimeter is going to be 2(4) + 3. This gives you 11 which you add to the 4.71 and get 15.71
Select the correct answer. Consider this function. Which graph represents the inverse of function f? The linear function on a coordinate plane passes through (4, 3), and (2, 2) which intercepts the axis at (0, 1), and (minus 2, 0). W. The linear function on a coordinate plane passes through (minus 4, 4), and (2, 1) which intercepts the axis at (4, 0), and (0, 2). X. The linear function on a coordinate plane passes through (3, 4), and (minus 1, minus 4) which intercepts the axis at (1, 0), and (0, minus 2). Y. The linear function on a coordinate plane passes through (minus 1, 4), and (2, minus 2) which intercepts the axis at (0, 2), and (0, 1). Z. A. W B. X C. Z D. Y
Answer:
A , C , D , i thinks it another one but ionk
Step-by-step explanation:
4. Use the formula for the area of a circle to derive the formula for the area of a sector.
The area of a circle to derive the formula for the area of a sector will be (θ/2π) x (area of the circle).
What is the area of the sector?Let r be the radius of the circle. Then the area of the circle will be
Area = πr²
Let r is the radius of the sector and θ be the angle subtends by the sector at the center. Then the area of the sector of the circle will be
Area = (θ/2π) πr²
Area = (θ/2π) x (area of the circle)
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which matrix can be used to solve the system
Answer:
6x + 7y = 14
7x + 8y = 27
6 7. x = 14
7 8. y = 27
option B
Need help please answer!!!
It can be modeled by an exponential function because each time x increases by 1, f(x) is multiplied by 4.
This means the base of the exponential function is 4, and since f(x)=3 when x=0, [tex]f(x)=3(4)^{x}[/tex]
A car travels at 80 km an hour. How far will it travel in 2 1/2 hours?
Find the solutions to x² = 8.
A. x- +4√6
B. x- +4√√2
C. x=+2√4
D. x=+2√2
Answer:
D. 2√2
Step-by-step explanation:
x² = 8
x = √8
x = √4 x √2
x = 2√2
Step-by-step explanation:
[tex] x {?}^{2} \sqrt{2 \times 2 \times 2} \\ \\ x { }^{2} = 2 \sqrt{2} [/tex]
What are the possible values of x in 8x² + 4x=-1? OA 2+1√2 3 -1±i 16 SOB. OC -1t с. 4 OD. 11 4 OE. 1ti√2 1+1/2 4 What are the possible values of x in 8x² + 4x = -1 ? OA 2 + 1√2 3 -1 ± i 16 SOB . OC -1t с . 4 OD . 11 4 OE . 1ti√2 1 + 1 / 2 4
Answer:
4
Step-by-step explanation:
4
The possible values of x are:
x = -1/2 + i/2
x = -1/2 - i/2
What is a quadratic equation?A basic quadratic equation, or a second-order polynomial equation with a single variable, is represented by the equation x : ax² + bx + c = 0, where a≠0 for the variable x. As it is a second-order polynomial equation, which is ensured by the algebraic fundamental theorem, it must have at least one solution.
To find the possible values of x in equation 8x² + 4x = -1, we need to solve for x.
First, we can rearrange the equation to get:
8x² + 4x + 1 = 0
We can solve this quadratic equation using the quadratic formula:
x = (-b ± √(b² - 4ac)) / 2a
where a, b, and c are the coefficients of the quadratic equation in standard form (ax² + bx + c).
In this case, a = 8, b = 4, and c = 1. Substituting these values into the quadratic formula, we get:
x = (-4 ± √(4² - 4(8)(1))) / 2(8)
x = (-4 ± √(16 - 32)) / 16
x = (-4 ± √(-16)) / 16
x = (-4 ± 4i) / 16
where i is the imaginary unit, which is defined as the square root of -1.
Therefore, the possible values of x are:
x = (-4 + 4i) / 16
x = (-4 - 4i) / 16
These values can also be simplified as:
x = -1/2 + i/2
x = -1/2 - i/2
So the possible values of x are complex numbers, specifically x = -1/2 ± i/2.
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Find the value below using your calculator. Round to the nearest hundredth. e³ Find the value below using your calculator . Round to the nearest hundredth . e³
The value of e³ = 20.079.
What is Euler's number , e ?e is an irrational number , It is a numerical constant used in mathematical constant .
The value of e = 2.718
It is asked in the question to determine the value of e³
Therefore
e³ = ( 2.718)³
e³ = 20.079
Therefore the value of e³ = 20.079.
The image of the calculation is attached with the answer.
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What is the surface area of the figure? 9 ft 9 ft 15 ft 15 ft 4 ft
The surface area of the given composite figure is; 528 ft²
How to find the area of a composite figure?To get the surface area of the attached composite shape, we will have to break the object down into smaller shapes to get;
Surface area 1 = 2(15 * 4) = 120 ft²
Surface area 2 = 2(9 * 4) = 72 ft²
Surface area 3 = 2(6 * 4) = 48 ft²
Surface area 4 = 2((15 * 15) - (9 * 9)) = 288 ft²
Thus;
Total surface area = 120 + 72 + 48 + 288
Total surface area = 528 ft²
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