The solution to the given inequality is [tex]b\leq 1.7[/tex]
InequalitiesFrom the question, we to determine the solution to the inequality.
To determine the solution of the inequality, we will determine the value of the variable. The variable in the given question is b.
The inequality can be solved as shown below.
[tex]\frac{7}{2} \geq b + \frac{9}{5}[/tex]
Multiply through by 10
That is,
[tex]10 \times \frac{7}{2} \geq 10\times b + 10\times \frac{9}{5}[/tex]
This becomes
[tex]5 \times 7 \geq 10b + 2 \times 9[/tex]
[tex]35 \geq 10b + 18[/tex]
Now, subtract 18 from both sides
[tex]35 - 18\geq 10b + 18-18[/tex]
[tex]17 \geq 10b[/tex]
This becomes,
[tex]10b \leq 17[/tex]
Divide both sides by 10
[tex]\frac{10b}{10} \leq \frac{17}{10}[/tex]
[tex]b\leq 1\frac{7}{10}[/tex]
OR
[tex]b\leq 1.7[/tex]
Hence, the solution to the given inequality is [tex]b\leq 1.7[/tex]
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A supervisor set the following performance goal for new employees: re-stock an average of 42 products per day for the entire work week (Monday thru Friday). Today is Friday and Employee A has re-stocked 185 products so far this week. How many products will Employee A need to re-stock today to meet the goal?
Answer:
25 more items
Step-by-step explanation:
Employees need to stock at least 42 each day for a whole week or work. (5 days) so wee need to find how much they need to stock in a week.
42 x 5 = 210.
So They need to stock 210. Employee A has already stocked 185. so we need to take 185 from 210 to see how MORE he needs to stock.
210 - 185 = 25.
25.
Hope this helped! Please mark as brainliest! THanks!
In order to be able to make the goal that was set for the employee, the employee would have to re-stock 25 products.
The worker is supposed to stack an average of 42 products from Monday to Friday which is 5 days.
Technically speaking, in every one of those 5 days, 42 products should be stocked. The total for the week is therefore:
= 5 days x Number of products stocked per day
= 5 x 42
= 210 products
The worker has stocked 210 products already and so is left with:
= Number to be stocked - Number already stocked
= 210 - 185
= 25 products
In conclusion, the worker still has to re-stock 25 products.
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After removing the outlier, what does the mean absolute deviation of this data set represent?
Correct answer gets brainliest
Answer:
3.2 inches
Step-by-step explanation:
1. The outlier is 23 inches, it is very big compared to the other numbers.
2. The average is 6 inches.
3. The deviations are: 4, 3, 5, 3, 1, 4, 4, 4, 3, and 1.
4. The mean of those numbers is 3.2 inches.
Answer:
THE ANSWER IS 3.2 INCHES
Step-by-step explanation:
Math , pls helppp ASAP
The tangent line AC forms a right angle with the radius line OC, so the angle at C is 90 degrees.
Angle O is given as 45 degrees, so angle A needs to equal:
180 - 90 - 45 = 45 degrees.
Which equation would best help solve the following problem?
Brett kicks a field goal with an initial vertical velocity of 42m/s.how long will it take the football to hit the ground?
Answer:
C
Step-by-step explanation:
You are making a couple of assumptions. The first is that since the given has units of m/s that requires an acceleration based in m/s^2. That eliminates choices A and B. 16 is usually associated with f/s^2
Second, you are assuming 42m/s is positive and the acceleration due to gravity is negative. It doesn't matter as long as they are opposite.
Third, you are assuming that 42 m/s is the vertical acceleration. If it is not then some sort of trigonometry is needed. Since your choices don't offer trig then this assumption must be taken care of.
So the correct answer is C.
A school sold small and large boxes of fruit for a fundraiser. One student sold 5 small boxes and 13 large boxes for $232. Another student sold 12 small boxes and 7 large boxes for $218. Their sales can be represented in two equations where x represents the price of the small boxes and y represents the price of the large boxes. Which constants can be multiplied by the equations so one variable will be eliminated when the systems are added together? Check all that apply.
The first equation can be multiplied by –12 and the second equation by 5 to eliminate x.
The first equation can be multiplied by 5 and the second equation by 12 to eliminate x.
The first equation can be multiplied by –7 and the second equation by 13 to eliminate y.
The first equation can be multiplied by 7 and the second equation by –13 to eliminate y.
The first equation can be multiplied by 12 and the second equation by –5 to eliminate x.
The first equation can be multiplied by 7 and the second equation by 13 to eliminate y.
Answer:
A,C,D,E
Step-by-step explanation:
Answer:
A,C,D,E are correct.
Step-by-step explanation:
Find the center, vertices, and foci of the ellipse with equation 2x2 + 8y2 = 16.
A) Center: (0, 0); Vertices: the point zero comma negative two square root two and the point zero comma 2 square root two ; Foci: Ordered pair 0 comma negative square root 6 and ordered pair 0 comma square root 6
B) Center: (0, 0); Vertices: (-8, 0), (8, 0); Foci: Ordered pair negative 2 square root 15 comma 0 and ordered pair 2 square root 15 comma 0
C) Center: (0, 0); Vertices: (0, -8), (0, 8); Foci: Ordered pair 0 comma negative 2 square root 15 and ordered pair 0 comma 2 square root 15
D) Center: (0, 0); Vertices: the point negative square root six comma zero and the point square root six comma zero ; Foci: Ordered pair negative square root 6 comma 0 and ordered pair square root 6 comma 0
Step-by-step explanation:
i think its B I'm not really sure
The value of a stock increases at a rate of 1/2% per year. If the initial value of the stock $40 a share, when will the value of the stock be $50? Round your answer to the nearest tenth of a year
Answer:
After 50 years the stock value will be $50 per share.
Step-by-step explanation:
Simple Interest Equation (Principal + Interest)
A = P(1 + rt)
Where:
A = Future amont = $50
P = Principal Amount = $40
r = Rate of Interest per year in decimal; r = R/100 = 0.5/100 = 0.005
t = Time Period involved in months or years
Plug in the values
50 = 40(1 + 0.005t)
50 / 40 = (1 + 0.005t)
5/4 = 1 + 0.005t
5/4 - 1 = 0.005t
0.25 = 0.005t
t = 0.25 / 0.005
t = 50 years
Answer:
44. 7 yr
Step-by-step explanation:
The compound interest equation is
[tex]A = P(1+ \frac{r }{ n})^{nt}[/tex]
You don't give the frequency of compounding, so I will assume that it is once per year.
Data:
P = $40
r = 0.5 % = 0.005
n =1
Calculations:
(a) Calculate A
A = P + I = 40 + 10 = $50
(b) Calculate t
[tex]50 = 40(1+ \frac{0.005 }{ 1})^{1 \times t}\\50 = 40(1+ 0.005)^{t}[/tex]
Divide each side by 40
[tex]1.25 = 1.005^{t}[/tex]
Take the logarithm of each side
log1.25 = tlog1.005
0.09691 = 0.002 166t
Divide each side by 0.002 166
t = 44.7 yr
The value of the stock will be $50 in 44.7 yr.
Help I’ll rate you brainliest
Answer:
5 strides because 6-1=5
Step-by-step explanation:
➷ You just need to count the number of squares. It would be 5 strides.
The mathematical way is using the y values:
6 - 1 = 5
It is 5 strides.
✽➶ Hope This Helps You!
➶ Good Luck (:
➶ Have A Great Day ^-^
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8+2(1+12÷2)^2
Please explain
Answer:
The best thing to do here is PEMDAS which is parenthesis, exponents, then eith multiply, divide, add, subtract which will help you figure out the answer and when you plug it all in you get 106 as ur answer
Step-by-step explanation:
Can you translate a mathemetical expression into a verbal expression?
Answer:
Yes, you can translate a mathemetical expression into a verbal expression.
Step-by-step explanation:
If that explantion was not helpful, you can always read out the equation verbally. For example, you can say that "three more than x" can be written as an algebraic expression. x + 3 x+ 3 x+3 .
find the values of a and b
Answer:
a = 115, b = 71
Step-by-step explanation:
The figure has one pair of parallel sides and is a trapezium.
Using a property of trapeziums
• each lower base angle is supplementary to the upper base angle on the same side.
a = 180 - 65 = 115
b = 180 - 109 = 71
A person has body fat percentage of 17.2% and weighs 171 pound how many pounds of her weight is made up of fat
Answer: 29.41 pounds
Step-by-step explanation:
You have the following information given in the problem:
- The fat percentage that the person has is 17.2%
- The person weighs 171 pounds.
Therefore, to calculate the amount of pounds of her weight is made up of fat (which you can call x), you must multiply the weight of the person by the fat percentage.
Therefore, you obtain the following result:
[tex]x=171lb*0.172\\x=29.41lb[/tex]
Which is the graph of the function f(x) = -√x?
Answer:
Step-by-step explanation:
The last (fourth) graph is that of the parent function y = √x. The negative sign in front of √x leads to reflection of this parent function graph in the x-axis. Thus, the correct graph of f(x) = -√x is the first one.
Quadrilateral A′B′C′D′ is a dilation of ABCD about point F.
What is the scale factor?
Answer:
The scale factor is 1.5
Step-by-step explanation:
we know that
If two figures are similar, then the ratio of its corresponding sides is proportional and this ratio is called the scale factor
so In this problem
Let
z -----> the scale factor
[tex]z=\frac{B'C'}{BC}=\frac{C'D'}{CD}=\frac{D'A'}{DA}=\frac{A'B'}{AB}[/tex]
substitute the values
[tex]z=\frac{3}{2}=\frac{4.5}{3}=\frac{4.5}{3}=\frac{4.5}{3}[/tex]
therefore
[tex]z=1.5[/tex]
The scale factor is 1.5
Solve the equation.
5x – 5 = 3x – 9
The answer is x = -2
Answer:
x=-2
Step-by-step explanation:
2x=-4
x=-2
which of the following graphs represents the equation above
y= 1/3x - 3
Graph y because your y intercept is equal to -3 so that’s where you would start. Then your slope is equal to rise over run so you would go up 1 unit and right 3 since it’s positive
Write the equation of the circle with center (7, 3) and a radius of 2.
A)(x - 7)2 + (y - 3)2 = 4
B)(x + 7)2 + (y + 3)2 = 4
C)(x - 7)2 + (y - 3)2 = 2
D)(x + 7)2 + (y + 3)2 = 2
A) would be the correct answer
what are the new coordinates of the figure aboge if it is reflected over the y axis?
The new coordinates of the figure is :
A=( 1,5) B= (-4,5) C= (-4,8)
Transformations on a Plane:A point on a plane can be subject to transformations. Examples of transformations that can be done on points are translations, reflections, or rotations about a point. These transformations are also observed algebraically, in which functions on the coordinates are applied.
Recall that if (x, y) is a point on the plane, reflecting it across the y-axis means that the x-coordinate is negated:
(x, y) => (-x, y)
The coordinates of the figure is
A = (-1,5)
B = (4, 5)
C = (4, 8)
The new coordinates of the figure is :
A=( 1,5) B= (-4,5) C= (-4,8)
This means that the first coordinate is changed, and the y-coordinate is left as is.
Therefore, it is the y-coordinate that stays the same when reflected across the y-axis.
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A (1, 5), B (-4, 5), C (-4, 8) are the new coordinates of the figure aboge if it is reflected over the y axis.
In the realm of plane geometry, various transformations can be applied to points, facilitating a means of altering their positions or orientations. These transformations include translations, reflections, and rotations, all of which have algebraic representations.
When reflecting a point across the y-axis, as denoted by the transformation (x, y) => (-x, y), the x-coordinate is negated while the y-coordinate remains unaffected.
This can be observed in the coordinates of the figure:
A (-1, 5)
B (4, 5)
C (4, 8)
After the reflection, the new coordinates become:
A (1, 5)
B (-4, 5)
C (-4, 8)
It is evident that the reflection operation results in the change of the sign of the x-coordinate while leaving the y-coordinate unaltered. Consequently, the y-coordinate remains the same when a point is reflected across the y-axis, illustrating a fundamental property of this geometric transformation.
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If there are 2,400 students,
52% are boys and 48% girls.
What is the ratio of boy and girl?
Answer:
13:12
Step-by-step explanation:
52% 2400 = 1248
48% 2400 = 1152
Reduce to 13/12 = 13:12
In the figure, lines m and n are parallel to each other. Lines p and q are also parallel to each other.
The value of x is ????? degrees, and the value of y is ??????? degrees.
The value of X is 112° and The value of Y is 68°
Answer:
Angle y: 68°
Angle x: 112°
Step-by-step explanation:
When you are dealing with two sets of parallel lines where one set intercepts the other, angles are always the same as the parallel line's angle. In this example
∡PM = 68° = ∡y°
Seeing that we now know that y is 68° and q is a straight line (Straight Lines have an angle of 180°) we can subtract 68° from 180° in order to get the degree of the angle x.
180° - 68° = 112°
Now we know that angle y is 68° and angle x is 112°
I hope this answered your question. If you have any more questions feel free to ask away at Brainly.
Write an expression from the words.
1. K less than 45
2. The product of 6 and k
3. The quotient of s and 4
4. The sum of 49 and t
A circle of yellow tulips is planted in Cedarburg's central park. Pam measured the circle and calculated that is has a circumference of 12.56 yards. What is the circle's diameter? Use 3.14 for .
Answer:
The circle's diameter is [tex]4\ yd[/tex]
Step-by-step explanation:
we know that
The circumference of a circle is equal to
[tex]C=\pi D[/tex]
where
D is the diameter of the circle
In this problem we have
[tex]C=12.56\ yd[/tex]
[tex]\pi=3.14[/tex]
substitute the values and solve for D
[tex]12.56=(3.14)D[/tex]
[tex]D=12.56/(3.14)=4\ yd[/tex]
Given a cone with a volume of 56.52 in^3 and height 7 in., find the base radius of the cone.Use 3.14 for pi. Round your answer to the tenths place. a. 2.1 in c. 4.9 in b. 2.8 in d. 4.3 in
Answer:
B
Step-by-step explanation:
Volume of Cone formula is given by : [tex]V=\frac{1}{3}\pi r^2 h[/tex]
Given V = 56.52 and h = 7, we plug them in and solve for r:
[tex]V=\frac{1}{3}\pi r^2 h\\56.52=\frac{1}{3}(3.14) r^2 (7)\\56.52=7.33r^2\\\frac{56.52}{7.33}=r^2\\7.71=r^2\\r=\sqrt{7.71}\\ r=2.77[/tex]
rounding to tenths place, r = 2.8 inches
Answer choice B is right
Answer: c. [tex]4.9\ in.[/tex]
Step-by-step explanation:
The volume of cone is given by :-
[tex]V=\dfrac{1}{3}\pi r^2 h[/tex], where r is radius and h is height of the cone.
Given: Height : 7 in.
Volume : [tex]56.52\ in^3[/tex]
Then the volume of the cone will be :-
[tex]56.52=\dfrac{1}{3}(3.14) r^2(7)\\\\\Rightarrow\ r^2=\dfrac{56.52\times3}{7\cdot3.14}\\\\\Rightarrow\ r^2=24.22285714\\\\\Rightarrow\ r=4.921672189\approx4.9\ in.[/tex]
Hence, the radius of the cone = [tex]4.9\ in.[/tex]
Find the volume, in cubic centimetes, of the rectangular prism pictured below...
Answer:
V=18.75 or 18 3/4
Step-by-step explanation:
The formula for a rectangle prism is V=L×W×H
V=L×W×H
V= 3×2.5×2.5
V=18.75 or 18 3/4
Find the value of x°
25°
85°
75°
105°
Answer:
x = 75 degrees
Step-by-step explanation:
155 and the angle next to it makes 180 degrees
To find the missing angle take 180 and subtract 155
180 - 155 = 25
All the angles in the upper triangle are 25, 80 and x
To find x add 80 and 25
80 + 25 = 105
A triangle equals 180 degrees so subtract 105 from 180 to get x
180 - 105 = 75
Hope this helps.
Answer: The angle is 75°
Step-by-step explanation:
Please give the other person brainliest, they deserve it :3
Find an equation in standard form for the hyperbola with vertices at (0, ±10) and asymptotes at y = ±five divided by four times x..
Answer:
The equation of the hyperbola in standard form is
[tex]\frac{y^{2}}{100}-\frac{4x^{2}}{625}=1[/tex]
Step-by-step explanation:
* We will take about the standard form equation of the hyperbola
- If the given coordinates of the vertices (0 , a) and (0 , -a)
∴ The transverse axis is the y-axis. (because x = 0)
- If the given asymptotes at y = ± (b/a) x
∴ Use the standard form ⇒ y²/a² - x²/b² = 1
* Lets use this to solve our problem
∵ The vertices are (0 , 10) and (0 , -10)
∴ a = ±10
∴ a² = 100
∵ The asymptotes at y = ± 5/4 x
∴ ± 5/4 = ± b/a
∵ a = ± 10
∴ ± 5/4 = ± b/10 ⇒ using cross multiplication
∴± (4b) = ± (5 × 10) = ± 50 ⇒ divide both sides by 4
∴ b = ± 25/2
∴ b² = 625/4
* Now Lets write the equation
* y²/100 - x²/(625/4) = 1
∵ x² ÷ 625/4 = x² × 4/625 = (4x²/625)
∴ y²/100 - 4x²/625 = 1
* The equation of the hyperbola in standard form is
[tex]\frac{y^{2}}{100}-\frac{4x^{2}}{625}=1[/tex]
If a day of the week is chosen at random, what is the probability of choosing Wednesday?
The probability of choosing Wednesday is 1/7
How to determine the probabilityThere are 7 days in a week, and one of the days is Wednesday.
So, we have:
Days = 7
Wednesday = 1
The probability of choosing Wednesday is calculated as:
P(Wednesday) =Wednesday/Days
This gives
P(Wednesday) = 1/7
Hence, the probability of choosing Wednesday is 1/7
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3km 9hm 9dam 19m +7km 7dam
10km+9hm+16adm+19m
I think your trying to question about combining the like terms?
The student is asked to add two sets of distances in various units. The sum of 3km 9hm 9dam 19m and 7km 7dam is converted to meters and added together, resulting in a total of 11 kilometers and 149 meters.
The question involves the addition of distances in different units, namely kilometers (km), hectometers (hm), decameters (dam), and meters (m). The student is asked to perform an addition of 3km 9hm 9dam 19m and 7km 7dam. To solve this, we must first convert all units to meters, add them up, and then convert back to the appropriate unit if necessary.
Step-by-step solution:
Convert each distance to meters:Add the distances in meters:If needed, convert back to mixed units:This results in a total distance of 11 kilometers and 149 meters.
1.32 repeating as a fraction
Answer:
[tex]\frac{131}{99}[/tex]
Step-by-step explanation:
Let
[tex]x=1.323232...[/tex]
Multiply x by a power of [tex]10[/tex], one that keeps the decimal part of the number the same:
[tex]100x=132.3232..[/tex]
Subtract [tex]x[/tex] from [tex]\\100x[/tex]
[tex]100x-x=132.3232...-1.3232...=131[/tex]
The repeating decimals should cancel out
[tex]\\99x=131[/tex]
solve for x
Divide by [tex]99[/tex] both sides
[tex]x=\frac{131}{99}[/tex]
f(x)=1/x-5, g(x)=5x-1/x A. Use composition to prove whether or not the functions are inverses of each other. B. Express the domain of the compositions using interval notation.
Answer:
Not inverse of each other
Domain : [-∞,0) U (0,5) U (5,∞]
Step-by-step explanation:
Given in the question two functions
f(x)=1/x-5
g(x)=5x-1/x
To find that each of them are inverse of each other we will use composition
f(g(x))[tex]\frac{1}{\frac{5x-1}{x}-5 }[/tex]
take LCM
[tex]\frac{1}{\frac{5x-1-5x}{x}}[/tex]
5x will be cancel
[tex]\frac{1}{\frac{-1}{x}}[/tex]
1 ÷ (-1/x)
1 × (-x/1)
-x
Now,
g(f(x))[tex]\frac{5\frac{1}{x-5} -1}{\frac{1}{x-5}}[/tex]
[tex]\frac{5}{x-5} -1}[/tex] × [tex]5-x[/tex]
[tex]\frac{5-x+5}{x-5} * (x-5)[/tex]
10-x
As it ended up with different answers, so f(x) and g(x) are not inverse of each other
The domain are all the possible x-values of function except x ≠ 0 and x ≠ 5
We can conclude that the domain of the composition function is
Domain : [-∞,0) U (0,5) U (5,∞]
To prove whether or not the functions f(x) = 1/(x-5) and g(x) = (5x-1)/x are inverses of each other, we need to show that their compositions result in the identity function. We also need to find the domain of the compositions f(g(x)) and g(f(x)).
Explanation:To prove whether or not the functions f(x) = 1/(x-5) and g(x) = (5x-1)/x are inverses of each other, we need to show that their compositions result in the identity function. Let's start by finding the composition f(g(x)):
Plug in g(x) into f(x): f(g(x)) = f((5x-1)/x)Simplify f(g(x)) by substituting (5x-1)/x into the expression for f(x)Simplify further to obtain the composition f(g(x)) as a function of xNow, we need to find the composition g(f(x)): g(f(x)) = g(1/(x-5))
Follow the same steps as above to simplify g(f(x)) as a function of x. If the compositions f(g(x)) and g(f(x)) both result in the identity function, then the functions f(x) and g(x) are inverses of each other.
To express the domain of the compositions f(g(x)) and g(f(x)), we need to consider the restrictions on the domains of the individual functions. The domain of f(g(x)) will be the values of x for which (5x-1)/x is defined, and the domain of g(f(x)) will be the values of x for which 1/(x-5) is defined.
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