2 The ratio of males to females in the class is 5 to 9. If the lunchroom has the same ratio but 45 females, how many males are in the lunchroom?
Answer:
Explanation:
From the question, we are given the ratio of males to females in the class as 5 to 9.
Total ratio = 5+9 = 14
Let the total number of student in the class be x. If there are 45 females then;
9/14 * x = 45
9x/14 = 45
Cross multiply;
9x = 14 * 45
x = 14 * 5
x = 70
Hence the total number of student in the class is 70
Get the number of male students;
Total students = Male + Female
70 = Male + 45
Male = 70-45
Male = 25
Answer:
Step-by-step explanation:
To get 45 females, you have to multiply 9 by a number. That number is 5 because 5 times 9 is 45. So what you do here is what you do with the other number, (5), so 5 times 5 is 25. That means there were 25 males in the lunchroom.
Solve the Exponential Function: [tex]x^2 * 2 - 2^x = 0[/tex]
Given the equation of the exponential function:
[tex]x^2\cdot2-2^x=0[/tex]We will solve the equation using the graph
the graph of the function is as shown in the following picture:
The solution to the equation will be the values of (x) at the point of intersection with the x-axis
As shown, there are 3 points of x-intercepts
So, the solution to the equation will be:
[tex]x=\mleft\lbrace-0.58,1,6.32\mright\rbrace[/tex]
7. Write an equation and solve. Round to the nearest hundredth where necessary.
19 is what percent of 40?
Answer:
47.5%
Step-by-step explanation:
Draw an angle in standard position inQuadrant I that has legs of 6 inches and 8inches.
Given:
There is an angle lying in quadrant II that has legs of 6 inches and 8 inches
The drawing of the angle will be as follows:
As shown in the figure the angle x lying in the quadrant II
And the legs of the right-angle triangle = 6 inches and 8 inches
Note: the legs can be reversed, which gives us another possible solution.
Use the graph to answer the question about discontinuity refer to image
Given the graph of the function
We will check the discontinuity of the function at x = -3
So, as shown in the graph :
as the function reach to x = -3 from the right and the left , the value of the function = -1
But at x = -3 , the function does not have a value
So, there is a discontinuity at x = -3, but can be removed if f(-3) = -1
So, the answer is : option A
There is a discontinuity that can be removed by defining f(-3) = -1
For each line the SLOPE between the 2 points given - simplify each fraction to prove that the lines have a CONSTANT rate of change : 1) Point T : 2) Point R : 3) Point S : 4) Slope of TR : 5) Slope of RS : 6) Slope of TS : 7) Describe the SLOPE of the line : 8) Therefore the CONSTANT RATE OF CHANGE IS ...?
the point T on the line is T(-7,6)
point R = R(-3,0)
point S = S(1,-6)
the slope of TR is
[tex]\begin{gathered} m=\frac{6-0}{-7-(-3)} \\ m=-\frac{6}{4} \\ m=-\frac{3}{2} \end{gathered}[/tex]slope of RS,
m = (0 - (-6))/(-3-1)
= - 6/4
= -3/2
slope of TS
m = (-6-6)/ 1-(-7)
= -12/ 8
= -3/2
the slope of the line or the constant rate of change is m = -3/2
Ten less than a number cubed is negative seven
We have
less than means subtract from
number cubed means elevate a number to power 3
therefore
Ten less than a number cubed is negative seven
is
[tex]x^3-10=-7[/tex]
Graph the following Y=x-4
Ok, so
We want to find the line:
[tex]y=x-4[/tex]First, remember that a line can be described with the following formula:
[tex]y=mx+b[/tex]Where "m" is its slope and b is its y-intercept.
Based in our equation, we got that m = 1 and b = - 4. So, we have a line with slope = 1, and y-intercept = -4.
To graph it, we have to take two points that lie on the line, and join them. We already know that the line has y-intercept at ( 0 , -4 ), so that's one point.
To find the other point, we could make y = 0 to find the x-intercept as follows:
[tex]\begin{gathered} y=x-4 \\ x-4=0 \\ x=4 \end{gathered}[/tex]Now, we have the x-intercept at (4 , 0) so that's other point.
We join both points:
So that's the graph for y = x-4.
Answer:
Step-by-step explanation:
1. When x is 0, y=-4, so plot the point (0,4) on the graph.
2. When y is 0, x=4, so plot the point (4,0) on the graph.
3. Draw a line between them and you're done.
What is the area of sector GHJ, given that θ= π/3 radians? Express your answer in terms of π and as a decimal rounded to the nearest tenth.
Answer:
[tex]\text{area of sector=4.7 square }\imaginaryI\text{nches}[/tex]Step-by-step explanation:
The area of a sector when the angle is measured in radians is represented by:
[tex]\text{ area of sector= }\frac{1}{2}r^2\theta[/tex]The given theta is pi/3, and the radius is 3 inches.
[tex]\begin{gathered} \text{ area of sector=}\frac{1}{2}*3^2*\frac{\pi}{3} \\ \text{ area of sector=}\frac{3}{2}\pi \\ \text{ Convert as a decimal rounded to the nearest tenth:} \\ \text{ area of sector= 4.7 square inches} \end{gathered}[/tex]Launch Problem The barista at Kellie's Coffee needs to make 10 12-ounce iced coffees. Each iced coffee is made with 2 ounces of oat milk, 8.2 ounces of cold brew coffee and 1.8 ounces of hazelnut flavoring. How much of each ingredient will be necessary to make the order of iced coffees? 2. How many ounces of cold brew coffee will be needed to make the order of iced coffee?
we have,
for 1 iced coffee:
2 ounces of oat milk
8.2 ounces of cold brew coffee
1.8 ounces of hazelnut.
then
answer 1:
for 10 iced coffee, we will need
2 x 10 = 20 ounces of oat milk
8.2 x 10 = 82 ounces of cold brew coffee
1.8 x 10 = 18 ounces of hazelnut flavoring
answer 2:
82 ounces of cold brew coffee are needed
For #'s 12 - 13, find the area of each figure.
Using the distance(d) formula to obtain the length AB,BC,CA.
The distance formula is,
[tex]d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]Given
[tex]\begin{gathered} A\rightarrow(5,-6) \\ B\rightarrow(-5,-3) \\ C\rightarrow(5,6) \end{gathered}[/tex]Therefore,
[tex]\begin{gathered} AB=\sqrt{(-5-5)^2+(-3--6)^2}=\sqrt{(-10)^2+(-3+6)^2}=\sqrt{100+3^2}=\sqrt{109} \\ BC=\sqrt{(5--5)^2+(6--3)^2}=\sqrt{10^2+9^2}=\sqrt{100+81}=\sqrt{181} \\ CA=\sqrt{(5-5)^2+(6--6)^2}=\sqrt{0^2+12^2}=\sqrt{144}=12 \end{gathered}[/tex]Therefore,
[tex]\begin{gathered} AB=\sqrt{109}=10.44030\approx10.4 \\ BC=\sqrt{181}=13.45362\approx13.5 \\ CA=12 \end{gathered}[/tex]Using Heron's formula to solve for the area
[tex]\begin{gathered} Area=\sqrt{s(s-a)(s-b)(s-c)} \\ s=\frac{a+b+c}{2} \end{gathered}[/tex]where,
[tex]\begin{gathered} a=10.4 \\ b=13.5 \\ c=12 \\ \\ s=\frac{10.4+13.5+12}{2}=17.95 \end{gathered}[/tex]Therefore, the area is
[tex]undefined[/tex]Question attached!!Answer choices 1. The graph has a relative minimum 2. The graph of the quadratic function has a vertex at (0,5)3. The graph opens up 4. The graph has one x- intercept 5. The graph has a y-intercept at (5,0)6. The axis of symmetry is x=0
Consider the following table:
this table represents the following graph:
According to this graph (parabola), and remembering that an absolute minimum is also a relative minimum:
we can conclude that the correct answer is:
Answer:1. The graph has a relative minimum 2. The graph of the quadratic function has a vertex at (0,5)3. The graph opens up 6. The axis of symmetry is x=0Simplify the expression 3^2/ 3^1/4 to demonstrate the quotient of powers property. Show any intermittent stepsthat demonstrate how you arrived at the simplified answer.
We are given a quotinet of two power expressions to be used to demonstrate the quotient property of powers:
[tex]\frac{3^2}{3^{\frac{1}{4}}}=3^2\cdot3^{-\frac{1}{4}}=3^{(\frac{8}{4}-\frac{1}{4})}=3^{\frac{7}{4}}[/tex]ANother way of doing it is to represent 3^2 as 3 to the power 8/4 so as to have the same radical expression.
Recall that fractional exponents are associated with radicals, and in this case the power "1/4" represents the fourth root of the base "3". That is:
[tex]3^{\frac{1}{4}}=\sqrt[4]{3}[/tex]So we also write 3^2 with fourth root when we express that power "2 = 8/4":
[tex]3^2=3^{\frac{8}{4}}=\sqrt[4]{3^8}[/tex]So now, putting that quotient together we have:
[tex]\frac{\sqrt[4]{3^8}}{\sqrt[4]{3}}=\sqrt[4]{\frac{3^8}{3}}=\sqrt[4]{3^7}=3^{\frac{7}{4}}[/tex]So we see that we arrived at the same expression "3 to the power 7/4"
in both cases. One was using the subtraction of the powers as the new power for the base 3, and the other one was using the radical form of fractional powers.
Find the equation of a line in the form y=Mx+b MATH HW
Using y=mx+b form first we calculate the slope.
We'll use points (0,-8) and (-8,0).
[tex]\begin{gathered} m=(-8-0)\div(0--8) \\ m=-\frac{8}{8} \\ m=-1 \end{gathered}[/tex]Next we calculate our b intercept
[tex]\begin{gathered} 0=-1(-8)+b \\ b=-8 \end{gathered}[/tex]So the equation is y=-x-8
Using the digits 1 to 9 at most one time each, fill in the boxes to make the equality true:
___ / ___ = ____ / ____ = ____
The complete equality will be;
⇒ 1 / 2 = 3 / 6 = 4 / 8
What is Proportional?
Any relationship that is always in the same ratio and quantity which vary directly with each other is called the proportional.
Given that;
By using the digits 1 to 9 at most one time each, fill in the boxes to make the equality true.
Now,
All the numbers from 1 to 9 are;
= 1, 2 ,3 , 4, 5, 6, 7, 8, 9
Let a proportion = 1 / 2
Hence, The equivalent ratio of 1/2 are;
= 3 / 6 and 4 / 8
Thus, The complete equality will be;
⇒ 1 / 2 = 3 / 6 = 4 / 8
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Wallpaper was applied to one rectangular wall of a large room. The dimensions of the wall are shown below. I will send the graph.
Given:
Wallpaper was applied to one rectangular wall of a large room. The dimensions of the wall is 42 feet and 25.5 feet.
Total cost of wallpaper was $771.12
Required:
What was the cost, in dollars, of the wallpaper per square feet.
Explanation:
We know the area of rectangle is length multiplied by breadth.
Here, we have
[tex]\begin{gathered} A\text{rea of wall =}42\times25.5 \\ =1071 \end{gathered}[/tex]Now,
The cost of wallpaper per square feet is
[tex]\begin{gathered} =\frac{771.12}{1071} \\ =0.72 \end{gathered}[/tex]Answer:
Hence, $0.72 is the answer.
evaluate and express answer in standard form.
4.56×3.6
________
0.12
The value of the given expression in the standard form is 1.368×10².
We are given a mathematical expression. The expression consists of two arithmetic operations. First of all, two numbers are multiplied by each other, and then their result is divided by the third number. Let the mathematical expression be denoted by the variable "E". The expression is given below.
E = (4.56×3.6)/0.12
First, we will multiply the numbers in the numerator.
E = 16.416/0.12
Now we will divide the numerator by the denominator.
E = 136.8
Hence, the value of the expression is 136.8. Now we need to convert the resulting number into standard form. The standard form is given below.
E = 1.368×10²
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Circle 1 is centered at (-4, -6) and has a radius of 9 centimeters. Circle 2 is centered at (4, 2) and has a radius of 6 centimeters. What is the scale factor?Which translation rule will translate Circle 1 to Circle 2?
For this type of problem we first notice that the center of the first circle has coordinates (-4,-6) and the center of the second one has coordinates (4,2) then all point of circle 1 (x,y) are translated according to the rule (x+8,y+8).
For the scale factor, we notice that the radius of circle 1 is 9 cm and the radius of circle 2 is 6cm then the scale factor is (2/3).
3/5 of a number is 18. What is the number
Let
x -----> the number
we have that
(3/5)x=18
solve for x
x=18*5/3
x=30
the number is 30Find the inverse of the function below and sketch by hand a graph of both the function and is inverse on the same coordinate plane. Share all steps as described in the lesson to earn full credit. Images of your hand written work can be uploaded. f(x)=(x+3)^2 with the domain x \geq-3
In order to find the inverse of f(x), let's switch x by f^-1(x) and f(x) by x in the function, then we solve the resulting equation for f^-1(x).
So we have:
[tex]\begin{gathered} f(x)=(x+3)^2 \\ x=(f^{-1}(x)+3)^2 \\ \sqrt[]{x}=f^{-1}(x)+3 \\ f^{-1}(x)=-3+\sqrt[]{x} \end{gathered}[/tex](The domain of f(x) will be the range of f^-1(x), so the range of f^-1(x) is y >= -3)
In order to graph the function and its inverse, we can use some points that are solutions to each one.
For f(x), let's use (-3, 0), (-2, 1) and (-1, 4).
For f^-1(x), let's use (0, -3), (1, -2) and (4, -1).
Graphing f(x) in red and f^-1(x) in blue, we have:
Graphing it manually, we have:
How would I solve 11 I’m confused on it I’m sorry I’m a bit slow
In order to better understand the question, let's draw an image representing the situation:
We want to find the distance x of this triangle. To do so, we can use the Pythagorean theorem, which states that the length of the hypotenuse squared is equal to the sum of each leg squared.
So we have:
[tex]\begin{gathered} 110^2=55^2+x^2 \\ 12100=3025+x^2 \\ x^2=12100-3025 \\ x^2=9075^{} \\ x=95.26\text{ ft} \end{gathered}[/tex]Rounding to the nearest tenth, we have a distance of 95.3 ft.
hich is the better buy? 2-quart carton of orange juice for $4.48 7-cup carton of orange juice for $3.64
According to the given data we have the following:
2-quart carton of orange juice=$4.48
7-cup carton of orange juice=$3.64
In order to find out what is the better choice to buy we would have to make the calculate the unit price.
2-quart carton of orange juice=$4.48,
Then unit price=$4.48/2
unit price=$2.24
7-cup carton of orange juice=$3.64
Then unit price=$3.64/7
unit price=$0.52
Therefore as the unit price of the 7-cup carton of orange juice is $0.52 and is lower than the unit price of $2.24 of the 2-quart carton of orange juice, hence, the better choice would be buying the 7-cup carton of orange juice.
Find the probability to generate a 4 digit even number from 1, 2, 3, 5.A.1/4B.1/2C.1D.0
give the following numbers
1, 2, 3, 5
we were asked to find the probability of generating a 4 digit even number from the numbers give above
recall,
Probabily = Number of possible outcome/Total number of outcomes
Number of possible outcome is = 1
Total number of outcomes is = 4
therefore,
Probability = 1/4
so the probability of generating a 4 digit even number from 1, 2, 3, 5 is 1/4
so the correct option is A which is 1/4
bea earned $ 11,700.00 commission for selling a house calculated at 6/100 of the selling price. what was the selling price of the house?
Given:
Commision earned = $11,700
The commission was calculated at 6/100 of the selling price.
To find the selling price of the house, we have the equation:
[tex]11700=\frac{6}{100}S[/tex]Where S represents the selling price of the house.
Let's solve for S.
Multiply both sides of the equation by 100:
[tex]\begin{gathered} 11700(100)=\frac{6}{100}S\ast100 \\ \\ 1170000=6S \end{gathered}[/tex]Divide both sides of the equation by 6:
[tex]\begin{gathered} \frac{1170000}{6}=\frac{6S}{6} \\ \\ 195000=S \\ \\ S=195000 \end{gathered}[/tex]Therefore, the selling price of the house is $195,000
ANSWER:
$195,000
find the missing length, assume that segments that appear to be tangent are tangent.
Since the side that measures 16 is tangent to the circle, it is perpendicular to the side that measures 12.
IT makes a right triangle.
Since it is a right triangle we can apply the Pythagorean theorem:
c^2 = a^2 + b^2
Where:
c= hypotenuse (longest side )= ?
a & b =the other 2 legs of the triangle.
Replacing:
?^2 = 12 ^2 + 16^ 2
Solve for the missing side:
?^2 = 144+256
?^2 = 400
?=√400
? = 20
1. Name one of the segments shown2.calculate their midpoint and lengths(as decimal rounded to the nearest tenth)3.identify all parallel segments
For naming a segment, we have to know its extrem points. If those extreme points are A and B, we name the segment as:
[tex]\bar{AB}[/tex]We are going to take as an example the segment with extreme points I and C, shown at the left above part of the image, so its name will be:
[tex]\bar{IC}[/tex]I need help with my math
Given an expression
[tex]\begin{gathered} y+\frac{3}{8}\text{ = }\frac{-2}{3}\text{ } \\ \text{collect like terms} \\ y=\text{ }\frac{-2}{3}\text{ - }\frac{3}{8} \\ y\text{ = }\frac{-16-9}{24} \\ \text{LCM = 24} \\ y=\text{ }\frac{-25}{24} \\ y=\text{ -1}\frac{1}{4} \end{gathered}[/tex]what is the volume of the sphere with a radius of 2 inches ?
The volume of a sphere is
[tex]\text{volume}=\frac{4}{3}\pi^{}^{}r^3[/tex]Therefore,
[tex]\begin{gathered} \text{volume}=\frac{4}{3}\times3.14\times2^3 \\ \text{volume}=33.4933333333=33.49\text{ cubic inches} \end{gathered}[/tex]Click an item in the list or group of pictures at the bottom of the problem and, holding the button down, drag it into the correct position in the answer box. Release your mouse button when the item is place. If you change your mind, drag the item to the trashcan. Click the trashcan to clear all your answers.Find the lateral area for the regular pyramid.L. A. =Find the total area for the regular pyramid.T. A. =
Answer
LA = 4√10
TA = 4 + 4√10
Step-by-step explanation
To find the Lateral Area (LA) of the pyramid, first, we need to calculate its slant height (s).
Considering the right triangle formed inside the pyramid, we can apply the Pythagorean theorem to find the length of s, as follows:
[tex]\begin{gathered} s^2=3^2+1^2 \\ s^2=9+1 \\ s=\sqrt{10} \end{gathered}[/tex]Now, we can calculate the lateral area as follows:
[tex]\begin{gathered} LA=\frac{1}{2}\times P\operatorname{\times}s \\ \text{ where P is the perimeter of the base of the pyramid. Substituting }P=4\times2\text{ and }s=\sqrt{10}: \\ LA=\frac{1}{2}\operatorname{\times}4\operatorname{\times}2\operatorname{\times}\sqrt{10} \\ LA=4\sqrt{10} \end{gathered}[/tex]To find the total area (TA) of the pyramid, first, we need to calculate the area of its base (B). In this case, the base is a square, then its area is:
[tex]\begin{gathered} B=b^2\text{ \lparen where b is the length of each edge\rparen} \\ B=2^2 \\ B=4 \end{gathered}[/tex]Finally, the total area is calculated as follows:
[tex]\begin{gathered} TA=B+LA \\ TA=4+4\sqrt{10} \end{gathered}[/tex]An item has a listed price form 45. If the sale tax rate is 9?% how much is the sales tax.
In order to calculate the sales tax to 45, calculate the 9% of 45, just as follow:
(9/100)(45) = 4.05
Hence, the sales tax is $4.05