A local hospital currently has 184 male patients. If the ratio of male to female patients is 4:3, how many female patients are there in the hospital?
There are 138 female patients in the hospital.
Solving word problems involving ratios.The solution to the word problem involving ratios in the given problem can be determined as follows.
From the given information:
The total number of people in the hospital = male + female
= 184 + x(unknown)
If the ratio of male to female is 4: 3. The total ratio is 4+3 = 7The ratio of males in the hospital is:
[tex]\mathbf{184= \dfrac{4}{7} \times x }[/tex]
[tex]\mathbf{184\times 7= 4 x }[/tex]
x = 322
The number of female patients in the hospital can now be computed as:
[tex]\mathbf{=\dfrac{3}{7}\times 322}[/tex]
= 138 female patients
Check:
The total number of people in the hospital is:
= 184 + 138
= 322 patients
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Factor by Grouping.
25x^2-20x-12
Answer:
ac = -300-20 = -30 +10(5x +2)(5x +(-6))Step-by-step explanation:
The sequence of required answers provides a step-by-step solution to the problem.
Factors of acIn the given trinomial, we identify the coefficients as ...
ax² +bx +c = 25x² -20x -12 ⇒ a=25; b=-20; c=-12
Then the ac product is ...
ac = (25)(-12) = -300
The factor pairs that make this product can be listed as ...
-300 = (-300)(1) = (-150)(2) = (-100)(3) = (-75)(4) = (-60)(5) = (-50)(6) = (-30)(10) = (-25)(12) = (-20)(15) . . . . (only pairs with a negative sum are listed)
The sums of these pairs are -299, -148, -97, -71, -55, -44, -20, -13, -5.
The factors of the ac product that add to -20 are -30 and 10.
Factor by groupingThese factors are used to rewrite the -20x term as a sum.
25x² -20x -12 = 25x² -30x +10x -12
Grouping these terms in pairs, we can identify common factors:
= (25x² -30x) +(10x -12)
= 5x(5x -6) +2(5x -6)
= (5x +2)(5x +(-6))
Write out the form of the partial fraction decomposition of the function. Do not determine the numerical values of the coefficients.[tex]\frac{t^4+t^2+1}{(t^2+4)(t^2+2)^2}[/tex]
The form of the partial fraction decomposition is [tex]\frac{At + B}{(t^2 + 4)} + \frac{Ct + D}{(t^2 + 2)} + \frac{Et + F}{(t^2 + 2)^2}[/tex]
How to decompose the function?The fraction is given as:
[tex]\frac{t^4 + t^2 + 1}{(t^2 + 4)(t^2 + 2)^2}[/tex]
To decompose the above, we make use of the following rule:
[tex]\frac{px^n + qx^m +....+ r}{(x^2 + a)(x^2 + b)^2} = \frac{Ax + B}{(x^2 + a)} + \frac{Cx + D}{(x^2 + b)} + \frac{Ex + F}{(x^2 + b)^2}[/tex]
So, we have:
[tex]\frac{t^4 + t^2 + 1}{(t^2 + 4)(t^2 + 2)^2} = \frac{At + B}{(t^2 + 4)} + \frac{Ct + D}{(t^2 + 2)} + \frac{Et + F}{(t^2 + 2)^2}[/tex]
Hence, the form of the partial fraction decomposition is [tex]\frac{At + B}{(t^2 + 4)} + \frac{Ct + D}{(t^2 + 2)} + \frac{Et + F}{(t^2 + 2)^2}[/tex]
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I’m so confused please help
Answer:
976cm squared
Step-by-step explanation:
that's all I could do .hope it helps. in case of any questions please ask.
Choose the letter of the equation for
the graph.
KIN
2
a. y =
sin x + 2
b. y = cos x + 2
c. y = cos(x - π)
d. y =
sin(x - π)
e. y = sin(x + π/2)
Enter
Answer:
a
Step-by-step explanation:
The midline is at y=2.
Eliminate c, d, e
Also, since there is no horizontal shift amongst the remaining options, we know that since y=2 when x=0, this means it must be a sine curve.
This means the answer is a.
factor equation step by step.
Answer:
no solution
Step-by-step explanation:
use grouping method:
f(x) = x^2 - 4x + 2
factor it:
when we try to factor the above equation, we see that there is no ordered pair in which the numbers multiple to -4 and add to 2, so there is no solution
answer the questions below to find the total surface area of the can
The total surface area of the tomato ketchup given in the diagram can be determined as follows:
The total surface area of a shape is the addition of the areas of its individual surface.
So that the questions can be answered as thus:
A. To find the area of the given circle;
i. Area of a circle = [tex]\pi r^{2}[/tex]
where r is the radius of the circle.
area of the circle = π[tex](2.5)^{2}[/tex]
= 6.25[tex]\pi[/tex]
ii. There are two identical circles in the cylinder.
iii. The total area of all circles = 2(6.25[tex]\pi[/tex])
= 12.5[tex]\pi[/tex] square inches
B. To find the area of the rectangle;
i. one side of the rectangle is 5 inches.
ii. The other side of the rectangle = 2[tex]\pi[/tex]r
= 2(2.5)[tex]\pi[/tex]
= 5[tex]\pi[/tex] inches
iii. The area of the rectangle = l x b
= 5[tex]\pi[/tex] x 5
= 25[tex]\pi[/tex] square inches
C. Total surfce area of the cylinder = 5[tex]\pi[/tex] + 25[tex]\pi[/tex]
= 30[tex]\pi[/tex] square inches
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Answer:
Step-by-step explanation:
First box
6.25
2
12.5
------
Second box
------
5
5
25
------
Last box
------
37.5
Solve-2x-8> 3x + 12.
A. x < -4
OB. x>-4
C. x > -3
D. x < -3
Answer:
x < -4
Step-by-step explanation:
add 8 to both sides
Simplify
Subtract 3x from both sides
Simplify, again
Multiply both sides by -1 ( reverse inequality)
Simplify, again
Divide both sides by 5
And vwola x < -4
HOPE THAT HELPS! :)
Margo borrows $1500, agreeing to pay it back with 3% annual interest after 18 months. How much interest will she pay?
Answer:
67.5
Step-by-step explanation:
I'm assuming this is simple interest.
1500x0.03x1.5=67.5
What are the slope and the y-intercept of the linear function that is represented by the table? x y Negative three-fourths Negative StartFraction 1 Over 30 EndFraction Negative one-half Negative StartFraction 2 Over 15 EndFraction One-fourth Negative StartFraction 13 Over 30 EndFraction Two-thirds Negative three-fifths a The slope is Negative two-fifths, and the y-intercept is Negative one-third. b The slope is Negative one-third, and the y-intercept is Negative two-fifths. c The slope is One-third, and the y-intercept is Negative two-fifths. d The slope is Two-fifths, and the y-intercept is Negative one-third.
The slope and the y-intercept of the function are: A. Slope = -2/5; y-intercept = -1/3.
How to Find Slope and Y-intercept of a Linear Function?Slope (m) = change in y / change in x.
Using two pairs of points form the table value, (1/4, -13/30) and (2/3, -3/5)"
Slope (m) = (-13/30 - (-3/5))/(1/4 - 2/3)
Slope (m) = (-13/30 + 3/5))/(1/4 - 2/3)
Slope (m) = (1/6)/(-5/12)
Slope (m) = (1/6)(12/-5) = 12/-30
Slope (m) = -2/5
Plug in m = -2/5 and (x, y) = (2/3, -3/5) into y = mx + b to find the y-intercept (b).
-3/5 = -2/5(2/3) + b
-3/5 = -4/15 + b
-3/5 + 4/15 = b
-1/3 = b
b = -1/3
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Answer:
A. Slope = -2/5; y-intercept = -1/3.
Step-by-step explanation:
Hope this helps!!
M=−8r
2
+11r−6
T=−7r
2
−9r+14
M
+
T
=
M+T=M, plus, T, equals
Your answer should be a polynomial in standard form.
M + T in standard form polynomial is -15r² + 2r + 8
How to represent polynomial in standard form?Polynomial in standard is when all its terms are arranged by decreasing order of degree.
Therefore,
M = - 8r²+ 11r - 6
T = -7r² - 9r + 14
M + T = - 8r²+ 11r - 6 + (-7r² - 9r + 14)
M + T = - 8r²+ 11r - 6 - 7r² - 9r + 14
combine like terms
M + T = - 8r² - 7r² + 11r - 9r - 6 + 14
In standard form, the polynomial is represented as follows;
M + T = -15r² + 2r + 8
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A high school baseball player has a 0.229 batting average. in one game, he gets 5 at bat. what is the probability he will get at least 2 hits in the game? round your answer to four places.
The probability he will get at least 2 hits in the game is 0.470
GivenThe batting average is 0.229
In one game he gets 5 at bat
To find the probability he will get at least 2 hits we use binomial distribution.
What is Binomial distribution?The binomial distribution is also a Frequency distribution used for the possible no. of successful outcomes in a given no. of trials in each of which there is the same probability of success.
So we have
n = 5
p = 0.299
q = 1 - p
= 0.701
[tex]P(X) = nC_{x} p^x q^(n-x)[/tex]
P(at least 2 hits in the game) = 1 - P(less than 2 hits)
= 1 - P(0) - P(1)
[tex]= 1 - 0.701^5 - 5C1 x 0.299 x 0.701^4[/tex]
= 1 - 0.169 - 0.361
= 0.470
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This is a cross-sectional view of candy bar ABC. A candy company wants to create a cylindrical container for candy bar ABC so that it is circumscribed about the
candy bar. If AD = 2.5 cm, what is the smallest diameter of wrapper that will fit the candy bar?
TheThe smallest diameter of wrapper that will fit the candy bar is 5cm.
Smallest diameterGiven:
AD = DC
AC = AD + DC
Segment AD = 2.5cm
Hence:
AC = AD + AD (AD = DC)
AC = 2AD
Where:
AD=2.5
So,
AC = 2(2.5cm)
AC = 5cm
Therefore the smallest diameter of wrapper that will fit the candy bar is 5cm.
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Answer: 5cm.
Step-by-step explanation:
Nadia says the hypotenuse of this right triangle has a length of 73 because the pythagorean theorem states that (28 45) squared = 73 squared. 3 squares are positioned to form a right triangle. the small square is labeled 28, medium square is 45, and large square is not labeled. which best describes nadia’s solution?
Both the options that Nadia gives are wrong about the length of hypotenuse.
Given length of hypotenuse is 73 and options which are :
1) Because the pythagoras theorem states that [tex]28^{2} +45^{2}[/tex] squared = 73 squared.
2) 3 squares are positioned to form a right triangle.
We have to choose the correct option which shows the calculation of length of hypotenuse.
Pythagoras theorem says that in a right angled triangle the square of hypotenuse of triangle is equal to sum of the square of base and square of perpendicular.
[tex]H^{2} =P^{2} +B^{2}[/tex]
First option says that [tex]28^{2} +45^{2} =73^{2}[/tex]
784+2025=5329
2809≠5329
so it is wrong.
Second option says that the length of hypotenuse is the sum of three squares but we have seen that the square of the length of hypotenuse is equal to sum of two square one is the square of base and the square of perpendicular.
Hence both the options are incorrect about the length of hypotenuse.
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Answer:
C
Step-by-step explanation:
To measure voltage (V), the formula V = √P. R is used. In this formula, P represents power measured in watts and
R represents resistance measured in ohms. What is the resistance (to the nearest ohm) if the volts are 130 and power is
1200 watts?
The resistance measured in ohms according to the given task is; 3.75 ohms.
What is the resistance in the given set-up?Since it follows that the three quantities are related by the formula; V = √P. R can be used to estimate the required resistance.
Hence, when V = 130 and P = 1200; we have;
130 = √1200 × R
R = 3.75 ohm
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A metallurgist has one alloy containing 45% copper and another containing 69% copper. How many pounds of each alloy must be use to make 42 pounds of a third alloy containing 66% copper
5.25 pounds of one alloy containing 45% copper and 36.75 pounds of 69% copper is used to make 42 pounds of 66% copper
What is an equation?An equation is an expression that shows the relationship between two or more variables and numbers.
Let x represent the amount of 45% copper and y represent the amount of 66% copper needed to make 42 pounds of a third alloy containing 66% copper. Hence:
x + y = 42 (1)
Also:
0.45x + 0.69y = 42(0.66) (2)
This gives:
x = 5.25, y = 36.75
5.25 pounds of one alloy containing 45% copper and 36.75 pounds of 69% copper is used to make 42 pounds of 66% copper
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What is the value of g(f(x)) when x=-2 if f(x)=x3
Answer:
The answer would be A: -15
what is the best estimate of the sum of the fraction? 31/4 +17/3 +8/18
The best estimate of the sum of the expression given is [tex]\rm 13 \dfrac {31}{26}[/tex]
What is a Fraction ?
A fraction is written as p/q , where q [tex]\rm \ne[/tex] 0
It is asked to determine the sum of the fraction
31/4 + 17/3 + 8/18
Taking the LCM of 4 , 3 , 18
LCM of 4 , 3 ,18 is 36
Therefore
[tex]\rm \dfrac{ 31 *9 + 17 *12 + 8 *2}{36 }[/tex]
(279+204+16) /36
499 / 36
[tex]\rm 13 \dfrac {31}{26}[/tex]
Therefore the best estimate of the sum of the expression given is [tex]\rm 13 \dfrac {31}{26}[/tex].
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which shows a correct step in using substitution to slove the system of equation y=2x-1 4x+y=2
The solution using correct step of substitution in the equation y=2x-1 4x+y=2 is x = 1/2 and y = 0
Simultaneous equationy = 2x - 1
4x + y = 2
Substitute the value of y in equation (1) into (2)4x + y = 2
4x + (2x - 1) = 2
4x + 2x - 1 = 2
6x - 1 = 2
6x = 2 + 1
6x = 3
x = 3/6
x = 1/2
substitute the value of x into equation (1)y = 2x - 1
y = 2(1/2) - 1
= 2/2 - 1
= 1 - 1
y = 0
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At Hinsdale College, students are employed by the college library to re-shelve books.
The students claim that a 15-minute coffee break every hour would relive boredom and
increase the average number of books re-shelved per hour. To test the student's claim,
the following data were gathered on a random sample of seven student employees.
Over a period of one week, each student worked a normal schedule without coffee
breaks. Then, during the next week, the students were allowed coffee breaks.
Unknown to the students, a member of the library staff secretly recorded the average
number of books shelved per hour and computed the averages with and without the
coffee break system. The results are below. Test the claim that the students shelve
more books when they have a coffee break, use a 0.05 level of significance.
Student 1 2 3 4 5 6 7
Without
Coffee
breaks
75 63 82 53 79 96 73
With
Coffee
Breaks
90 72 95 50 85 110 89
The p value is less, therefore one should reject the null hypothesis.
How to illustrate the information?From the information given, the test statistic will be:
t = (10 - 0)/(6.733/✓7)
t = 3.930.
The degree of freedom will be:
= 7 - 1 = 6
Using the table, the p value will be 0.0039.
Since the p value is less than 0.05 one should reject the null hypothesis.
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NEED HELP ASAP
there should be a picture giving you info
Answer:
to find this radius you need to square the area and divide it by pi or 3.14 if your using Alex
put the events in order of what is most likely to happen, to least likely to happen. If you were to win a million dollars for winning one of these events, which would you pick to play? Use probability to explain your answers
Answer:
no man you should reconsider the question again
try typing again i guess its wrong
Step-by-step explanation:
no man you should reconsider the question again
try typing again i guess its wrong
winning a lottery would be correct one i guess
Which of the following illustrates the truth value of the following conditional?
p: 7 + 1 = 0
q: 2 + 2 = 5
F F → T
T T → T
F T → F
T F → T
The truth table for implication of the equations is F F ⇒ T
What is a truth table?A truth table is a mathematical logic table that shows the truth values of different logic statements combined by a given logic rule.
Analysis:
P: 7 +1 is not equal to 0 making P to be false(F)
q: 2+2 is not equal to 5 making q to be false(F)
so for conditional or implication, F F⇒ T
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Solve the quadratic equation by using the quadratic formula. If the solutions are not real, enter NA.
2x2−7x+1=0
Enter the exact answers.
The field below accepts a list of numbers or formulas separated by semicolons (e.g. 2;4;6 or x+1;x−1 ). The order of the list does not matter.
Enclose numerators and denominators in parentheses. Remember that (a−b)/1+n is not the same as (a−b)/(1+n) .
By using the quadratic formula, the roots of the quadratic equation 2 · x² - 7 · x + 1 are represented by the irrational number x = (7 ± √41) / 4.
How to find the roots of quadratic equation by quadratic formula
For polynomials of the form a · x² + b · x + c = 0, the two roots can be found analytically by quadratic formula, whose expression is described below:
[tex]x = \frac{-b \pm \sqrt{b^{2}-4\cdot a\cdot c}}{2\cdot a}[/tex]
If we know that a = 2, b = - 7 and c = 1, then the roots of the polynomial are:
x = 7/4 ± (1/4) · √41
x = (7 ± √41) / 4
By using the quadratic formula, the roots of the quadratic equation 2 · x² - 7 · x + 1 are represented by the irrational number x = (7 ± √41) / 4.
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If 3 times a certain number is increased by 4 the result is 28. What is the number?
If x is "the number," which of the following equations could be used to solve for the number?
3 x + 4 = 28
3 x = 4 + 28
3( x + 4) = 28
Answer:3x+4=28
Step-by-step explanation:
the second one would equal 3x=32
And the third one would equal 3x+12=28 which isn’t right either
3. Which graph represents the solution to 13k-21> 7?
Answer: Option (2)
Step-by-step explanation:
[tex]|3k-2| > 7[/tex] means [tex]3k-2 < -7[/tex] or [tex]3k-2 > 7[/tex].
Solving each of these cases gives [tex]k < -\frac{5}{3}[/tex] or [tex]k > 3[/tex].
So, the answer is Option (2).
5. Lucinda is a babysitter. Her hourly rate is $5.00. fin one week, she baby sat 13 hours and
received tips of $14.50. How much did she earn?
MD writes an order for Lortab Elixir 5mg by mouth as needed for pain every 4 hours. Pharmacy dispenses you with 7.5mg/15ml. How many tablespoons will you administer per dose?
Following the prescription, You will need to administer a 0.7 tablespoon per dose.
Determining the number of tablespoons by using equivalent expressions?We can determine the number of tablespoons that are administered by using equivalent expressions.
From the standard conversion rate, we know that:
1 ml = 0.067628 tbsp15 ml = 1.01442 tbspUsing equivalent expressions:
7.5 mg/1.01442 tbsp = 5 mg/x tbsp
x = (1.01442 × 5)/7.5 tbsp
x = 0.67 tbsp
x = 0.7 tbsp per dose.
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What is addition and subtraction
[tex]\huge\text{Hey there!}[/tex]
[tex]\huge\textsf{What is addition \& subtraction?}[/tex]
[tex]\huge\textbf{What is addition?}[/tex]
[tex]\bullet\large\textbf{ Well, \underline{addition} simply means when you're ADDING}\\\large\textbf{2 or more numbers from each other to get the result of}\\\large\textbf{a number.}[/tex]
[tex]\huge\textbf{Random notes}[/tex]
[tex]\star\large\textbf{ Usually, you start working with addition when you're in}\\\large\textbf{pre-kindergarten (pre-k also known as head-start)}\\\\\star\large\textbf{ When, you're adding you are going upward.}\\\\\star\large\textbf{ Addition sometimes come after you learn how to count}\\\large\textbf{the basic numbers and so forth because adding never}\\\large\textbf{ends if you really think about.}[/tex]
[tex]\huge\textbf{Example:}[/tex]
[tex]\heartsuit\large\textbf{ 2 \boxed{\bf +} 5 = 7}\\\\\\\heartsuit\large\textbf{ You got the result of 7 because you started at 2 \& went}\\\larg\textbf{up 5 spaces to your right on your number and you landed}\\\large\textbf{on 7.}[/tex]
[tex]\huge\textbf{What is subtraction?}[/tex]
[tex]\bullet\large\textbf{ Well, subtraction simply means you're taking away. Often}\\\large\textbf{people call it take aways.}[/tex]
[tex]\huge\textbf{Random notes:}[/tex]
[tex]\star\large\textbf{ Usually, you start working with subtraction when you're}\\\large\textbf{in pre-kindergarten (pre-k also known as headstart)}\\\\\star\large\textbf{When you're subtracting you are doing downward.}\\\\\star\large\textbf{You focus more on subtraction when you're counting}\\\large\textbf{backwards.}[/tex]
[tex]\huge\textbf{Example:}[/tex]
[tex]\heartsuit\large\textbf{ 7 \boxed{\bf -} 5 = 2 }\\\\\\\heartsuit\large\textbf{ 7 \boxed{\bf -} 2 = 5}\\\\\\\heartsuit\large\textbf{ For equation \#1. you begin at 7 and go BACK 5 spaces}\\\large\textbf{and you should have landed on 2.}\\\\\\\heartsuit\large\textbf{ For equation \#2. you begin at 7 \& go BACK 2 spaces}\\\large\textbf{and you should have landed on 5.}[/tex]
[tex]\huge\textsf{KEEP IN MIND:}[/tex]
[tex]\circ\large\textsf{ Addition OPPOSITE is subtraction \& subtraction OPPOSITE is}\\\large\textsf{addition.}[/tex]
[tex]\huge\text{Good luck on your assignment \& enjoy your day!}[/tex]
~[tex]\frak{Amphitirite1040:)}[/tex]
What is the following quotient?
2
√13+√11
O√13-2√11
√13+√11
6
O
113 + √11
12
O
● √13 - √11
[tex]\frac{2}{\sqrt{13}+\sqrt{11}} \times \frac{\sqrt{13}-\sqrt{11}}{\sqrt{13}-\sqrt{11}}\\\\=\frac{2\sqrt{13}-2\sqrt{11}}{13-11}\\\\=\boxed{\sqrt{13}-\sqrt{11}}[/tex]
The solution is: our final quotient is: (√13 - √11).
What is multiplication?In mathematics, multiplication is a method of finding the product of two or more numbers. It is one of the basic arithmetic operations, that we use in everyday life.
here, we have,
Explanation
Since we have radicals in the denominator, we need to rationalize our expression.
To do it we just need to multiply both numerator and denominator by the conjugate of the denominator.
Remember that the conjugate of a binomial is the same binomial with the sing in between changed.
given that,
2/ (√13 + √11)
Now, we can simplify the denominator:
multiplying by (√13 - √11)
we get,
2 * (√13 - √11) / (√13 + √11)* (√13 - √11)
The only radical that we can simplify in the numerator is , which simplifies to:
2 (√13 - √11) / 13 - 11
= 2(√13 - √11) /2
= (√13 - √11)
So, our final quotient is: (√13 - √11)
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