[tex]4x - 7x - 4x + 7 \sqrt{x} + \sqrt{x} [/tex]
[tex] - 7x + 8 \sqrt{x} [/tex]
A survey of 400 nurses yielded the following information: 279 were health club members, 215 were smokers, and 160 of the health club members were smokers. how many of the 400 surveyed nurses were health club members or were smokers?
Health club members or were smokers is [tex]334[/tex] from a A survey of [tex]400[/tex] nurses yielded.
How can we find the health club members or were smokers ?
Events of health club members is [tex]P(M)=279[/tex]
Events of smokers is [tex]P(S)=215[/tex]
Probability of health club members and smokers is [tex]p(M and S)=160[/tex]
Probability of health club members or were smokers is =?
So we use the formula
[tex]p(M or S)=p(M)+p(S)-p(M and S)\\ = 279+215-160\\ = 334[/tex]
Probability of health club members or were smokers is [tex]334[/tex]
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A)x=45
B)x=90
C)x=20
D)x=4.5
Answer:
x=4.5
Step-by-step explanation:
We know that if all sides are congruent then all angles must also be congruent, therefore you can solve for x with the following equation:
[tex]20x=90[/tex]
Solve
[tex]x=4.5[/tex]
Match each system of equations to the inverse of its coefficient matrix, A-1, and the matrix of its solution, X.
The system of equations to the inverse of its coefficient matrix, A⁻¹, and the matrix of its solution, X is shown in the figure.
Given that the system of equations are shown in given figure.
The first system of equations are
[tex]\begin{aligned}4x+2y-z&=150\\x+y-z&=-100\\-3x-y+z&=600\\\end[/tex]
By writing in matrix AX=b, we get
Coefficient matrix [tex]A=\left[\begin{array}{lll}4&2&-1\\1&1&-1\\-3&-1&1\end{array}\right][/tex] and [tex]B=\left[\begin{array}{l}150&-100&600\end{array}\right][/tex]
Firstly, we will find the A⁻¹ by finding the determinant and adjoint of A and divide the adjoint with determinant, we get
[tex]\begin{aligned}|A|&=\left|\begin{array}{lll}4&2&-1\\1&1&-1\\-3&-1&1\end{array}\right|\\ &=4(1-1)-2(1-3)-1(-1+3)\\&=4(0)-2(-2)-1(2)\\ &=2\neq 0\end[/tex]
[tex]\begin{aligned}Adj A&=\left[\begin{array}{lll}0&2&2\\-1&1&-2\\-2&3&2\end{array}\right]^T\\&=\left[\begin{array}{lll}0&-1&-2\\2&1&3\\2&-2&2\end{array}\right]\end[/tex]
[tex]\begin{aligned}A^{-1}&=\frac{Adj A}{|A|}\\ &=\left[\begin{array}{lll}0&-0.5&-0.5\\1&0.5&1.5\\1&-1&1\end{array}\right]\end[/tex]
For a solution Consider [A B] and apply row operations, we get
[tex]\begin{aligned}\left[A\right.\text{ }\left.B\right]&=\left[\begin{array}{lll1}4&2&-1&150\\1&1&-1&-100\\-3&-1&1&600\end{array}\right]\\ R_{2}&\rightarrow 4R_{2}-R_{1},R_{3}\rightarrow 4R_{3}+3R_{1}\\ &\sim \left[\begin{array}{lll1}4&2&-1&150\\0&2&-3&-550\\0&2&1&2850\end{array}\right]\\ R_{3}&\rightarrow R_{3}-R_{2}\\ &\sim \left[\begin{array}{llll}4&2&-1&150\\0&2&-3&-550\\0&0&4&3400\end{array}\right]\end[/tex]
Thus, [tex]x=\left[\begin{array}{l}x\\y\\z\end{array}\right]=\left[\begin{array}{l}-250\\1000\\850\end{array}\right][/tex]
The second system of equations are
[tex]\begin{aligned}x+y-z&=220\\5x-5y-z&=-640\\-x+y+z&=200\\\end[/tex]
Similarly, we will find for second system of equations
[tex]\begin{aligned}|A|&=\left|\begin{array}{lll}1&1&-1\\5&-5&-1\\-1&1&1\end{array}\right|\\ &=1(-5+1)-1(5-1)-1(5-5)\\&=1(-4)-1(4)-1(0)\\ &=-8\neq 0\end[/tex]
[tex]\begin{aligned}Adj A&=\left[\begin{array}{lll}-4&-4&0\\-2&0&-2\\-6&-4&-10\end{array}\right]^T\\&=\left[\begin{array}{lll}-4&-2&-6\\-4&0&-4\\0&-2&-10\end{array}\right]\end[/tex]
[tex]\begin{aligned}A^{-1}&=\frac{Adj A}{|A|}\\ &=\left[\begin{array}{lll}0.5&0.25&0.75\\0.5&0&0.5\\0&0.25&1.25\end{array}\right]\end[/tex]
[tex]\begin{aligned}\left[A\right.\text{ }\left.B\right]&=\left[\begin{array}{llll}1&1&-1&220\\5&-5&-1&-640\\-1&1&1&200\end{array}\right]\\ R_{2}&\rightarrow R_{2}-5R_{1},R_{3}\rightarrow R_{3}+R_{1}\\ &\sim \left[\begin{array}{llll}1&1&-1&220\\0&-10&4&-1740\\0&2&0&420\end{array}\right]\\ R_{3}&\rightarrow 5R_{3}+R_{2}\\ &\sim \left[\begin{array}{llll}1&1&-1&220\\0&-10&4&-1740\\0&0&4&360\end{array}\right]\end[/tex]
Thus, [tex]x=\left[\begin{array}{l}x\\y\\z\end{array}\right]=\left[\begin{array}{l}100\\210\\90\end{array}\right][/tex]
The third system of equations are
[tex]\begin{aligned}2x+2y-z&=290\\x+y-3z&=500\\x-y+2z&=600\\\end[/tex]
Similarly, we will find for third system of equations
[tex]\begin{aligned}|A|&=\left|\begin{array}{lll}2&2&-1\\1&1&-3\\1&-1&2\end{array}\right|\\ &=2(2-3)-2(2+3)-1(-1-1)\\&=2(-1)-2(5)-1(-2)\\ &=-10\neq 0\end[/tex]
[tex]\begin{aligned}Adj A&=\left[\begin{array}{lll}-1&-5&-2\\-3&5&4\\-5&5&0\end{array}\right]^T\\&=\left[\begin{array}{lll}-1&-3&-5\\-5&5&5\\-2&4&0\end{array}\right]\end[/tex]
[tex]\begin{aligned}A^{-1}&=\frac{Adj A}{|A|}\\ &=\left[\begin{array}{lll}0.1&0.3&0.5\\0.5&-0.5&-0.5\\0.2&-0.4&0\end{array}\right]\end[/tex]
get
[tex]\begin{aligned}\left[A\right.\text{ }\left.B\right]&=\left[\begin{array}{llll}2&2&-1&290\\1&1&-3&500\\1&-1&2&600\end{array}\right]\\ R_{2}&\rightarrow 2R_{2}-R_{1},R_{3}\rightarrow 2R_{3}-R_{1}\\ &\sim \left[\begin{array}{llll}2&2&-1&290\\&0&-5&710\\0&-4&5&910\end{array}\right]\end[/tex]
Thus, [tex]x=\left[\begin{array}{l}x\\y\\z\end{array}\right]=\left[\begin{array}{l}479\\-405\\-142\end{array}\right][/tex]
Hence, each system of equations to the inverse of its coefficient matrix, A⁻¹, and the matrix of its solution, X.
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In circuit training, exercises are usually set up so that the same muscle group is worked in back to back exercises.
In circuit training, exercises are usually set up so that the same muscle group is worked in back to back exercises is a "false" statement.
What is circuit training?A circuit workout consists of six or more exercises that are alternated with brief rest intervals and performed for either a predetermined number of reps or a certain duration of time.
Some features of circuit training exercise are-
It is a great approach to increase muscular strength and endurance as well as cardiovascular health. Due to the brief rest times, the use of major muscles in conjunction with smaller ones, and the mix of upper, lower, and whole-body movements in circuit training, your heart rate will increase and remain elevated during the entire circuit.Once all of the selected exercises have been finished, a circuit has been completed. A single training session may involve several circuits.Benefits of doing circuit training exercise-
Training in strength.Cardiovascular Health, Time Efficiency, Friendly Environment, Avoids BoredomTo know more about the circuit training, here
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The complete question is -
In circuit training, exercises are usually set up so that the same muscle group is worked in back to back exercises.(True/False)
Show your steps in evaluating each of the following expressions. The steps count 4 points each, the answer is 1
The steps in evaluating each of the following expressions is shown below.
What is an expression?An expression is a mathematical equation which shows the relationship that exist between two or more numerical quantities or variables.
How to evaluate the given expressions?15 - 35/7 - 2 + 3 - 4
15 - (35/7) - 2 + 3 - 4 (bracket and division)
15 - 5 - 2 + 3 - 4 (regroup)
15 + 3 - 5 - 2 - 4 (subtract and add)
18 - 11 = 7.
Expression 2.10 + 2(9 - 5) - 16/18
10 + (2 × 4) - 8/9 (bracket and division)
10 + 8 - 8/9 (add)
18 - 8/9 (subtract)
162/9 - 8/9 = 17 1/9 or 154/9.
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Complete Question:
Show your steps in evaluating each of the following expressions. The steps count 4 points each, the answer is 1 point.
A. 15 - 35/7 -2 + 3 -4
B. 10 + 2(9 - 5) - 16/18
Find the surface area of the prism. Round to the nearest tenth if necessary.
The surface area of the prism according to the segment labels is; 480mm².
What is the surface area of the prism?The prism given in the task content is five-faced and hence, its surface area can be evaluated as follows;
Surface area = 2(0.5×15×8)+(15×9)+(8×9) + (17×9).
Hence, the surface area of the prism upon evaluation is; 480mm².
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laura goes for a cycle from her house to the post office 4km away work out laura's speed cycling to the post office CORBETTMATHS 2016
ItItItIt takes Laura 15 minutes (0.25 hours) to cycle to the post office.
Speed and timea. It takes Laura 15 minutes (0.25 hours) to cycle to the post office.
b. Speed:
Speed=Distance/Time
Speed=4/0.25
Speed=16 km/hr
c. It takes Laura 20 minutes to cycle to the post office.
d. Time
Time=20 minutes (1/3 hour)
Speed:
Speed=Distance/Time
Speed=4÷1/3
Speed=12 km/hr
Therefore It takes Laura 15 minutes (0.25 hours) to cycle to the post office.
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The propeller blades on a submarine have a radius of 6 feet. At full speed, they turn at 120 revolutions per minute. What is the angular velocity, in radians per minute, at the tip of the blade? Round your answer to the nearest hundredth.
Using proportions, it is found that the angular velocity at the tip of the blade is of 753.98 radians per minute.
What is a proportion?A proportion is a fraction of a total amount, and the measures are related using a rule of three.
Each revolution has [tex]2\pi[/tex] radians, hence in one minute, the 120 revolutions will have a measure in radians of:
M = 120 x 2pi = 240pi = 753.98
Hence the angular velocity is of 753.98 radians per minute.
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If 4x² = 16, then x =
A20
B12
C4
D2
h(n) = 41 - 5n
Complete the recursive formula of h(n).
h(1) =
h(n) = h(n-1)
The recursive formula of h(n) is h(1) = 36 and h(n) = h(n -1) - 5
How to determine the recursive formula?The function is given as:
h(n) = 41- 5n
Calculate h(1) and h(2)
h(1) = 41- 5(1)
h(1) = 36
h(2) = 41- 5(2)
h(2) = 31
Calculate the difference between h(1) and h(2)
d = 31 - 36
d = -5
This means that:
h(1) = 36 and h(n) = h(n -1) - 5
Hence, the recursive formula of h(n) is h(1) = 36 and h(n) = h(n -1) - 5
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Brainliest for answer
A quadratic equation is graphed to the left. Which of the following equations could be paired with the graphed equation to create a system of equations whose solution set is comprised of the points (2,-4)and (-4,2)?
The linear function that goes through the points (2,-4) and (-4,2) is:
y = -x + 2.
What is a linear function?A linear function is modeled by:
y = mx + b
In which:
m is the slope, which is the rate of change, that is, by how much y changes when x changes by 1.b is the y-intercept, which is the value of y when x = 0, and can also be interpreted as the initial value of the function.A linear function going through the points (2,-4) and (-4,2) would intersect the parabola at these points, hence these points would be the solution for the system of equations.
The slope of the line is:
m = (-4 - 2)/(2 - (-4)) = -1.
The line goes through point (2,-4), that is, when x = 2, y = -4, which we use to find the y-intercept b.
y = -x + b
-4 = -2 + b
b = -2.
Hence the equation is:
y = -x + 2.
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what is the area for the green square?
The perimeter of a deck is 33 at the length of the deck is 10 feet what is the width of the deck
The width of the deck is 6.5 feet.
The perimeter of a two-dimensional shape is the total length of the outline. To find the perimeter of a rectangle, we add the lengths of all four sides. Since opposite sides of a rectangle are always equal, we need to find the dimensions of length and width to find the perimeter of a rectangle. We can write the perimeter of the rectangle as twice the sum of its length and width. The perimeter is a linear measure and has units as meters, centimeters, inches, feet, etc.
Assuming the deck is rectangle
Perimeter = 2(length + width)
33ft = 2 (10 + width)
16.5 = 10 + width
width = 6.5 ft
Thus the width of the deck is 6.5 feet.
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The picnic breakfast cost $12. Jasmine left a tip that was 15 percent of the
cost of the meal. How much money was the tip that Jasmine left?
PLEASE HELP WILL GIVE BRAINLIEST
Arrange the tiles on both boards to find the value of x.
Board sum: 3x + (-5) = 1
What x value solves the equation?
3x - 5 = 1
X =
Answer: x = 2
Step-by-step explanation:
3x - 5 = 1
add 5 to both sides
3x - 5 (+5) = 1 (+5)
3x = 6
divide by 3 on both sides
3x/3 = 6/3
x = 2
?? math-domain and range
Answer:
Domain: All real numbers (infinite) Range: [tex]y \leq -4[/tex]
Step-by-step explanation:
For the domain, the x-axis will continue to be used for the parabola, because the parabola can go on forever and can use an x- value on the x-axis. For the range, the largest number the parabola will go up to is -4. Therefore, if that is the highest point/ where the vertex is, the highest point on the y-axis is -4, resulting in the answer y can be equal to or less than -4 (y [tex]\leq[/tex] -4), since the parabola will continue to go down with the reflection over the x-axis.
what is the range of the function of graph?
a.) all real numbers
b.) all real numbers greater than or equal to 0
c.) all real numbers greater than or equal to 1
d.) all real numbers greater than or equal to 2
The correct answer is "all real numbers greater than or equal to 2".
Select the correct answer.
A container is made by cutting off the bottom of a cone. The container has a diameter of 30 centimeters and a height of 20 centimeters. The
small cone that was removed has a diameter of 10 centimeters and a height of 6 centimeters.
What is the volume of the container, to the nearest cubic centimeter?
A. 6,126 cm³
B. 6,283 cm³
C. 5,812 cm³
D. 5,969 cm³
The volume of the container is 5969 cm³. The correct option is D. 5,969 cm³
Calculating VolumeFrom the question, we are to determine the volume of the container
Volume of the container = Volume of the cone - Volume of the small cone
The volume of a cone is given by the formula,
V = 1/3πr²h
Where V is the volume
r is the radius
and h is the height
From the given information,
For the small cone,
Diameter = 10 cm
∴ Radius, r = 10cm/ 2 = 5 cm
h = 6 cm
For the big cone
diameter = diameter of the container = 30 cm
∴ Radius = 30cm/ 2
Radius = 15cm
h = height of small cone + height of container
h = 6 cm + 20 cm
h = 26 cm
Putting the parameters into
Volume of the container = Volume of the cone - Volume of the small cone
We get,
Volume of the container = 1/3π × 15² ×26 - 1/3π × 5² × 6
Volume of the container = 1/3π (15² ×26 - 5² × 6)
Volume of the container = 1/3π (5850 - 150)
Volume of the container = 1/3π (5700)
Volume of the container = 1/3 × π × 5700
Volume of the container = 5969.026 cm³
Volume of the container ≈ 5969 cm³
Hence, the volume of the container is 5969 cm³. The correct option is D. 5,969 cm³
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Please help me
The sum of an integer and its square is 210. Find the integer. Include a completer
solution
Answer:
14
Step-by-step explanation:
An integers are whole numbers and their opposites. ...-3,-2,-2,0,1,2,3...
I just played with the numbers and found that 14 + 14^2 (14 squared is 14 x 14).
14 + (14)(14) = 210
Answer:
refer to the attachment
Will give you brilliantest
PLEASE ANSWER ASAP
What is the solution to the following system of equations?
Answer:
(-3, 1)
Step-by-step explanation:
the easiest thing to do is look at the graph and find the point where the two lines intersect
A super sundae ice cream cone has a radius of 0. 5 in and a depth of 4 in. A wonderful waffle cone has a radius 0. 9 in and a depth of 3 in. Which cone holds more ice cream?
The wonderful waffle cone holds more ice cream than super sundae cone.
In this question,
The ice cream cone is the shape of hemisphere at the top and cone shape at the bottom.
Volume of ice cream cone = volume of hemisphere + volume of cone
Volume of ice cream cone = [tex]\frac{2}{3}\pi r^{3} +\frac{1}{3} \pi r^{2} h[/tex]
Volume of super sundae cone:
Radius of hemisphere = height of hemisphere = 0.5 in
Depth of the ice cream cone = 4 in
Volume of super sundae cone = [tex]\frac{2}{3}\pi (0.5)^{3} +\frac{1}{3} \pi (0.5)^{2} (4)[/tex]
⇒ [tex]\frac{2}{3}(3.14)(0.125) +\frac{1}{3} (3.14)(0.25)(4)[/tex]
⇒ 0.2616+1.0466
⇒ 1.3082 ≈ 1.31 cubic in.
Volume of wonderful waffle cone:
Radius of hemisphere = height of hemisphere = 0.9 in
Depth of the ice cream cone = 3 in
Volume of wonderful waffle cone = [tex]\frac{2}{3}\pi (0.9)^{3} +\frac{1}{3} \pi (0.9)^{2} (3)[/tex]
⇒ [tex]\frac{2}{3}(3.14)(0.729) +\frac{1}{3} (3.14)(0.81)(3)[/tex]
⇒ 1.526+2.5434
⇒ 4.0694 ≈ 4.07 cubic in.
Thus volume of wonderful waffle cone > volume of super sundae cone.
Hence we can conclude that the wonderful waffle cone holds more ice cream than super sundae cone.
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A square has a side of length 2xcm. in terms of X, what is the area
Answer:
4x^2
Step-by-step explanation:
2x(2x) It is a square so we multiply the side by the side to get the area.
=2*x*2*x
=4*x2
=4x^2
Using the equation y = 2x - 3, what would the input need to be for an output of 7?
00
O 11
05
08
help me please omg im in a rush
Answer:48
Step-by-step explanation:
Brett had 3/4 of a family sized pizza. he gave each of his brothers half of this. what fraction of the pizza was each brother given?
Answer:
[tex]\frac{3}{8}[/tex]
Step-by-step explanation:
[tex]\frac{3}{4}[/tex] * [tex]\frac{1}{2}[/tex] = [tex]\frac{3}{8}[/tex]
Oscar bought some markers, notebooks, and packs of sticky notes for his office. He bought the same number of markers as notebooks. He bought three more packs of sticky notes than markers and notebooks combined. He paid $1.05 for each marker, $2.25 for each notebook, and the packs of sticky notes were $1.95. How many of each kind of office supply did Oscar buy if he paid $49.05 in all?
Using a system of equations, it is found that Oscar bought 6 markers, 6 notebooks and 15 packs of sticky notes.
What is a system of equations?A system of equations is when two or more variables are related, and equations are built to find the values of each variable.
In this problem, the variables are:
Variable x: Number of markers.Variable y: Number of notebooks.Variable z: Number of packs of notes.He bought the same number of markers as notebooks, hence:
x = y.
He bought three more packs of sticky notes than markers and notebooks combined, hence:
z = 3 + x + y
z = 3 + 2x.
He paid $1.05 for each marker, $2.25 for each notebook, and the packs of sticky notes were $1.95. He spent $49.05 in total, hence:
1.05x + 2.25y + 1.95z = 49.05.
Then:
1.05x + 2.25x + 1.95(3 + 2x) = 49.05.
7.2x = 43.2
x = 43.2/7.2
x = 6.
The amounts are as follows:
y = 6.z = 3 + 2(6) = 15.He bought 6 markers, 6 notebooks and 15 packs of sticky notes.
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The reference angle for is, which has a terminal point of (2).
What is the terminal point of ?
(-²)
(-4/2, 4/2)
○ B. (2,-²)
(-2/²2,-4/2)
OA
A.
O C.
○ D. (22)
Answer: C
Step-by-step explanation:
[tex]\frac{5\pi}{4}[/tex] is in the third quadrant, so both x and y are negative.
Therefore, the only possible answer is C.
At a coffee shop, the manager recorded the number of customers who visited the store at the end of each hour. The graph shows the recordings for a 24-hour period. The function describing this graph is a transformation of the parent sine function, y=sin(x)
Which value is closest to the amplitude of the transformed function?
O 83 customers
O 27 customers
O 54 customers
O 30 customers
Answer:
Step-by-step explanation:
The amplitude of a sine function is equal to one-half the distance between the maximum and minimum values of the function.
In this case, the maximum value is approximately 84 customers, and the minimum value is approximately 30 customers
Therefore, the value that is closest to the amplitude of the transformed function is 27 customers.
There are 120 students in class 7. it is known that 2 3 out of them like maths, out of which 35 are girls. also, out of total students, 3 5 are boys. (3) (a) what is the number of girls in the class? (b) how many students like maths? (c) how many boys like maths?
maths questions can be solved using unitary method.
Answer:
(a) The total number of girls in the class are 48
(b) The total number of students that like maths are 80
(c) The total number of boys like maths are 45
Solution:
According to the question, [tex]\frac{3}{5}[/tex] of total students are boys
number of boys = [tex]\frac{3}{5}[/tex] × 120 = 72
Also, According to the question, [tex]\frac{2}{3}[/tex] of total students like maths
number of students = [tex]\frac{2}{3}[/tex] × 120 =80
(a) The total number of girls in the class = total number of students - total number of boys
total number of girls in the class = 120 - 72 = 48
(b) The total number of students that like maths are 80
(c) The total number of boys like maths = total number of students that like maths - total number of girls that like maths
total number of boys like maths = 80 - 35 = 45
What is unitary method?
The unitary approach is a strategy for problem-solving that involves first determining the value of a single unit, then multiplying that value to determine the required value.
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