Step-by-step explanation:
Given
Principal = $1,800
interest rate = 5.5%
Using the below formula to calculate the mortgage
[tex]\begin{gathered} m\text{ = }\frac{p\cdot\text{ r (}1+r)^n}{(1+r)^n\text{ - 1}} \\ \text{Where P = principal, r = interest rate} \\ m\text{ = \$1800} \\ r\text{ = 5.5\% } \\ r\text{ = }\frac{5.5}{100}\text{ = 0.055} \\ \text{ since it is per month, hence the interest rate is given as} \\ r\text{ = }\frac{0.055}{12}\text{ = 0.00458} \\ n\text{ = 12 }\cdot\text{ 30} \\ n\text{ = 360} \\ 1800\text{ = }\frac{P\cdot0.00458(1+0.00458)^{360}}{(1+0.00458)^{360}\text{ - 1}} \\ 1800\text{ = }\frac{P\cdot0.00458(1.00458)^{360}}{(1.00458)^{360}\text{ - 1}} \\ 1800\text{ = }\frac{P\cdot0.00458\cdot\text{ 5.1812}}{5.1812\text{ - 1}} \\ 1800\text{ = }\frac{P\cdot\text{ 0.0237}}{4.1812} \\ \text{Cross multiply} \\ 1800\cdot\text{ 4.1812 = P }\cdot\text{ 0.0237} \\ 7526.16\text{ = P }\cdot\text{ 0.0237} \\ p\text{ = }\frac{7526.16}{0.0237} \\ P=\text{ \$317, 559. 50} \end{gathered}[/tex]Hence, the loan he can afford is $317, 559. 50
Part B
The total money he will pay to the bank is calculated as follows
Total amount = 1800 * 360
Total amount = $648, 000
22.2: X's Y'S Match each expression in column A with an equivalent expression from column B. Be prepared to explain your reasoning. А 1.1934) Buty 1. 12(x+y) the w 2. 12(x - y) w 2. (9x + 5y)-(3x + 7y) 3. (9x + 5y)-(3x - 7y) 3.6(x - 2y) 4. 9x - 7: + 3x + 5y 4. 9x + 5y + 3x - 7 5. 9x - 7y + 3x - 5y 5.9x + 5y - 3x + 7y 6.9x - 7y - 3x - 5y 6.9x - 3x + 5y - 7y
Given data:
The given list.
1) The first expression can be written as,
[tex]\begin{gathered} 9x+5y+3x+7y=12x+12y \\ =12(x+y) \end{gathered}[/tex]2) The second expression can be written as,
[tex](9x+5y)-(3x+7y)=9x-3x+5y-7y[/tex]3)The third expression can be written as,
[tex](9x+5y)-(3x-7y)=9x+5y-3x+7y[/tex]4)The fourth expression can be written as,
[tex]9x-7y+3x+5y=9x+5y+3x-7y[/tex]5)The fifth expression can be written as,
[tex]\begin{gathered} 9x-7y+3x-5y=12x-12y \\ =12(x-y) \end{gathered}[/tex]6)The sixth expression can be written as,
[tex]\begin{gathered} 9x-7y-3x-5y=6x-12y \\ =6(x-2y) \end{gathered}[/tex]Thus, the correct match is 1-1, 2-6, 3-5, 4-4, 5-2, 6-3.
Complete the function table for the given domain, and plot the points on the graph. (t) = -12 + 2.1 + 5 -1 0 1 2 3 Drawing tools Click on a tool to begin draving. EK Select f(x) Point Click on the Graph to place a Point HHHH 6 2 2 10 0
f(x) = -x^2 + 2x + 5
x -1 0 1 2 3
f(x) 2 5 6 5 2
-5|x+4|-7 describe the transformation.
Answer:3
Step-by-step explanation:
so you take 41 and divide by 2 and get 5. then take -51 and times by 6 which is 24.then you take seven and multipy by 3 and get 20. so you are left with 5, 24, and 20. Multiply all of them and get 3!!
The formula for calculating the distance, d, in miles that one can see to the horizon on a clear day is approximated by d=1.22radical x, where x is the elevation in feet of a person's eyes. a. approximately how far, to the nearest mile, can a person whose eyes are 600 feet above sea-level see? b. approximately how high, to the nearest foot, would a person's eyes need to be to see 100 miles?
The expression to calculate the distance a person can see is below, where x is the height in feet of a person's eyes above see-level:
[tex]d=\sqrt[1.22]{x}\lbrack mi\rbrack[/tex]a) A person who is 600 feet height will see:
[tex]d=\sqrt[1.22]{600}=189.30mi[/tex]b) In order to get the height a person needs to be so that he/she could see 100 miles long, we solve the equation for x:
[tex]\begin{gathered} d=x^{\frac{1}{1.22}} \\ d^{1.22}=(x^{\frac{1}{1.22}})^{1.22}=x \\ x=100^{1.22}=275.42ft \end{gathered}[/tex]I need help with this practice problem solving This subject is trig from my ACT prep guide I will add an additional picture of the answer options
Connect the points in a smooth curve, approaching the asymptotes located where the tangent function is undefined.
Given the table below, write a linear equation that defines the dependent variable, c, in terms of the independent variable, a.
For a linear equation, the first step is to find the slope.
Based on the table, I see that every time "t" increases by 1, then "k" increases by 4.
Since we're told k is the dependent variable, the slope will be
[tex]\dfrac{\text{change in }k}{\text{change in }t}} = \dfrac{4}{1} = 4[/tex]
The slope is always [tex]\dfrac{\text{change in dependent variable}}{\text{change in independent variable}}[/tex].
Once you have the slope, you need the vertical (We'd normally call this this y-intercept, but there's no "y" here. You could call it the "k" intercept in this example.)
From the table, we again see that t=0 has k=2, so that 2 is the value we need.
This gives us our equation: k = 4t + 2.
(This all is really just the slope-intercept form with x's now being called "t" and y's now being called "k".)
For nitrogen to be a liquid, its temperature must be within 12.78 °F of –333.22 °F. Which equation can be used to find the maximum and minimum temperatures at which nitrogen is a liquid, x?
The maximum and minimum temperatures at which nitrogen is a liquid is -320.44°F and = -346°F.
What is an equation?An equation is the statement that illustrates that the variables given. In this case, two or more components are taken into consideration to describe the scenario.
Since the nitrogen to be a liquid, its temperature must be within 12.78 °F of –333.22 °F.
The minimum temperature will be:
= -333.22 - 12.78
= -346°F
The maximum temperature will be:
= -333.22 + 12.78
= -320.44°F
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The box plot shows the average monthly high temperatures in New York City for 12 months. What is the difference between the range and interquartile range of the temperatures data?
The difference between the range and interquartile range of the temperatures data is equal to 16.
What is a range?Mathematically, range can be calculated by using this formula;
Range = Highest number - Lowest number
Range = 84 - 38
Range = 46.
What is an interquartile range?Mathematically, interquartile range (IQR) is the difference between first quartile (Q₁) and third quartile (Q₃):
IQR = Q₃ - Q₁
Based on the given box and whisker plot (see attachment), we can logically deduce the following quartile ranges:
Third quartile, Q₃ = 48
First quartile, Q₁ = 78
Now, we can calculate the interquartile range (IQR) is given by:
Interquartile range, IQR = Q₃ - Q₁
Interquartile range, IQR = 78 - 48
Interquartile range, IQR = 30
For the difference, we have:
Difference = Range - IQR
Difference = 46 - 30
Difference = 16
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What is the value??8+(-3)+15-(-40)
We applied the rules that said:
- If we add a negative number, it is the same as substracting its negative. That is why "+(-3)" is equal to "-3".
- If we substract a negative number is equal to add the negative of this number. That is why "-(-40)" is equal to "+40".
A dairy needs 396 gallons of milk containing 6% butterfat. How many gallons each of milk containing 8% butterfat and milk containing 2% butterfat must be used to obtain the desired 396 gallons?
ANSWER:
264 gallons of milk containing 8% butterfat
132 gallons of milk containing 2% butterfat
STEP-BY-STEP EXPLANATION:
From the statement we can propose the following system of equations:
Let x be the milk that contains 8% butterfat and let y be the 2%.
[tex]\begin{gathered} x+y=396\rightarrow y=396-x\text{ (1)} \\ 0.08x+0.02y=0.06\cdot396\rightarrow0.08x+0.02y=23.76\text{ (2)} \end{gathered}[/tex]We substitute in equation (1) in equation (2) and substitute for x, just like this:
[tex]\begin{gathered} 0.08x+0.02\cdot(396-x)=23.76 \\ 0.08x+7.92-0.02x=23.76 \\ 0.06x=23.76-7.92 \\ x=\frac{15.84}{0.06} \\ x=264 \end{gathered}[/tex]Knowing the value of x, we can calculate the value of y, substituting in equation 1, like this:
[tex]\begin{gathered} y=396-264 \\ y=132 \end{gathered}[/tex]Therefore, 264 gallons of milk containing 8% butterfat and 132 gallons of milk containing 2% butterfat are needed.
Peter is thinking of a number. If he adds 23 to that number, the sum is 31.A. Write an algebraic equation you can use to find Peter’s number. Let n be Peter’s number.
Try It! On Saturday, the vacation resort offers a discount on water sports. To takea surfing lesson and go parasailing costs $130. That day, 25 people takesurfing lessons, and 30 people go parasailing. A total of $3,650 is collected.What is the discounted price of each activity?CHECK ANSWER
Let the cost of surfing lesson be x and the cost of Parasiling be y
From the question, both surfing lesson and parasailing cost $130
Hnece;
x + y = 130 ---------------------------(1)
From the question, 25 people take surfing lesson and 30 pupil went for parasailing and a total of $3, 650 was collected
Hence;
25x + 30y = 3650--------------------------------(2)
We can now solve equation (1) and (2) simultaneously
Using elimination method,
multiply through equation(1) by 30
30 x + 30 y = 3900 ------------------(3)
subtract equation(1) from equation (3)
5x = 250
divide both-side of the equation by 5
x = 50
substitute x = 50 into equation (1) and then solve for y
x + y = 130
50 + y = 130
subtract 50 from both-side of the equation
y = 130 - 50
y =80
Therefore, the discount price of Surfing lesson is $50 while the discount price for parasailing is $80
What is the complement of a 54 1/2 degree angle
Two angles are complementary if their sum is 90 degrees
Therefore, to get a complement of 54 1/2 degrees, we will have to subtract it from 90 degrees
Let the complement of 54 1/2 be represented by x
[tex]\begin{gathered} x=90-54\frac{1}{2} \\ \\ x=90-\frac{109}{2} \\ \\ x=\frac{180-109}{2} \\ \\ x=\frac{71}{2} \\ \\ x=35\frac{1}{2}\text{ degrees} \end{gathered}[/tex]Therefore, the complement of angle 54 1/2 degrees is angle 35 1/2 degrees
Solve the following equation:
-3(5+4x)-7=14
The value of x is, x = -3.
What is solving an equation?
A General Rule for Equation Solving
Remove parentheses from each side of the equation and combine similar phrases to make it simpler.
To separate the variable term on one side of the equation, use addition or subtraction.
To find the variable, use division or multiplication.
Consider, the given equation
-3(5 + 4x) - 7 = 14
Solving the parenthesis
-15 - 12x - 7 = 14
Simplifying,
-22 - 12x = 14
Adding 22 on both sides,
-22 - 12x + 22 = 14 + 22
-12x = 36
Divide both sides by 12,
-12x/12 = 36/12
-x = 3
Multiply both sides by -1.
-x(-1) = 3(-1)
x = -3
Hence, the value of x is, x = -3.
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A 104° sector of a circle has an area of 56 square centimeters. Tothe nearest centimeter, what is the diameter of the circle?
The diameter is 8cm
Explanation:Given the following:
[tex]\begin{gathered} \theta=104^o \\ \\ \text{Area(}A)=\pi r^2=56cm^2 \\ \text{Diameter(D)}=2r=\text{?} \end{gathered}[/tex]From the area of the circle, we can have the value for the radius, r as follows:
[tex]\begin{gathered} \pi r^2=56 \\ r^2=\frac{56}{\pi} \\ \\ r=\sqrt[]{\frac{56}{\pi}}\approx4cm \end{gathered}[/tex]We can now obtain the diameter by multiplying the radius by 2
[tex]D=2r=2\times4=8cm[/tex]a laptop was originally sold for %975 the laptop is now on sale for $828.75 what is the percent markdown
The percent markdown is of the 15% of the price.
What is the percent markdown?We know that the original price is $975, and at the moment is sold by $828.75.
If we define the markdown (as a decimal) as r, then we can write the equation:
$828.75 = $975*(1 - r)
Solving this for r, we get:
($828.75 - $975)/(-$975) = r = 0.15
To write this as a percentage, we just need to multiply this by 100%.
0.15*100 = 15%
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sally, a journalism student, counted the number of pages in several major magazines. Number of pages Number of magazines 118 4 152 4 169 2 is the number of pages that a randomly chosen magazine had. What is the expected value of X? write your answer as a decimal.
Let's begin by identifying key information given to us:
4 magazines have 118 pages
4 magazines have 152 pages
2 magazines have 169 pages
The expected value for X (in pages) is given by:
[tex]\begin{gathered} P(118pages)=\frac{4}{10}=\frac{2}{5} \\ P(152pages)=\frac{4}{10}=\frac{2}{5} \\ P(169pages)=\frac{2}{10}=\frac{1}{5} \\ EV(x)=118\times\frac{2}{5}+152\times\frac{2}{5}+169\times\frac{1}{5} \\ EV(x)=141\frac{4}{5}=141.80 \\ EV(x)=141.8 \end{gathered}[/tex]The expected value of X is 141.8 pages
I’m the diagram below, C is the midpoint of AB. If AC is 4 centimeters, what is the length of CBA.4cmB.8cmC.6cmD.2cm
Consider that a mid-point is at equal distances from each end of the line segment.
Given that C is the mid point of AB, so point C must be at equal distance from ends A and B,
[tex]AC=CB[/tex]Given that AC measures 4 centimeters,
[tex]AC=4\text{ cm}[/tex]Substitute the value,
[tex]CB=4\text{ cm}[/tex]Therefore, option A is the correct choice.
x=72+(m*14)when m=6 to the third power
The value of x is 3096
Here, we want to find the value of x when m is 6 raised to its third power
We proceed as follows;
[tex]\begin{gathered} m=6^3\text{ = 216} \\ Substitute\text{ this value} \\ x\text{ = 72}+\text{(216 }\times\text{ 14)} \\ x\text{ = }72\text{ + 3024} \\ x\text{ = 3096} \end{gathered}[/tex]A park walkway surrounds a fountain as shown. Find the area of the walkway. Round to the nearest foot.
The fountain is depicted by the white circle in the picture. The surrounding walkway is depicted by the grey areas.
From the sketch shown above, the semi-circle inscribed in the rectangle is one half of the fountain. We shall calculate the area of the semi-circle and subtract this from the area of the rectangle.
The area of the rectangle is;
[tex]\begin{gathered} \text{Area}=l\times w \\ \text{Area}=30\times42.5 \\ \text{Area}=1275ft^2 \\ \text{The area of the semicircle is,} \\ \text{Area=}\frac{1}{2}(\pi\times r^2) \\ \text{The diameter is 18 ft, and therefore the radius is 9 ft} \\ \text{Area}=\frac{1}{2}(3.14\times9^2) \\ \text{Area}=\frac{1}{2}(3.14\times81) \\ \text{Area}=\frac{1}{2}(254.34) \\ \text{Area}=127.17ft^2 \end{gathered}[/tex]Therefore, the area of the shaded region would be,
Area = 1275 - 127.17
Area = 1147.83
Next step is to calculate the other half of the figure (the right side), as follows;
Observe that the outer semi-circle is the shaded region while the inner one is the white portion.
The area is
[tex]\begin{gathered} \text{Shaded region;} \\ \text{Area}=\frac{1}{2}(\pi\times r^2) \\ \text{Area}=\frac{1}{2}(3.14\times15^2) \\ \text{Area}=\frac{1}{2}(3.14\times225) \\ \text{Area}=\frac{1}{2}(706.5) \\ \text{Area}=353.25ft^2 \\ \text{White region;} \\ \text{Area}=\frac{1}{2}(\pi\times9^2) \\ \text{Area}=\frac{1}{2}(3.14\times81) \\ \text{Area}=127.17ft^2 \end{gathered}[/tex]The area of the shaded region is;
Area = 353.25 - 127.17
Area = 226.38
Therefore the total area of the walkway surrounding the fountain is;
Area = 1147.83 + 226.38
Area = 1374.21
Area = 1,374 feet squared (rounded to the nearest foot)
Instructions: For the following quadratic functions, write the function in factored form and then find the -intercepts, axis of symmetry, vertex, and domain and range. Round to one decimal place, if necessary.
Factored form: y = (x+1)(x-8)
x-intercept: (-1, 0) and (8, 0)
Axis of symmetry: x = 7/2
Vertex: (7/2, -81/4)
Domain: All real numbers
Range: y ≥ -81/4
Explanations:Given the quadratic equation expressed as:
[tex]y=x^2-7x-8[/tex]Factorize
[tex]\begin{gathered} y=x^2-8x+x-8 \\ y=x(x-8)+1(x-8) \\ y=(x+1)(x-8)\text{ Factored form} \end{gathered}[/tex]The x-intercept is the point where y= 0. Substitute y = 0 into the factored form
[tex]\begin{gathered} (x+1)(x-8)=0 \\ x=-1\text{ }and\text{ }8 \\ The\text{ x-intercept are \lparen-1, 0\rparen and \lparen8, 0\rparen} \end{gathered}[/tex]The axis of symmetry of the equation is given as x = -b/2a where:
a = 1
b = -7
Substitute:
[tex]\begin{gathered} axis\text{ of symmetry:}x=\frac{-(-7)}{2(1)} \\ axis\text{ of symmetry: }x=\frac{7}{2} \end{gathered}[/tex]The vertex form of the equation is in the form (x-h)^2+k where (h, k) is the vertex. Rewrite in vertex form:
[tex]\begin{gathered} y=x^2-7x-8 \\ y=x^2-7x+(-\frac{7}{2})^2-(-\frac{7}{2})^2-8 \\ y=(x-\frac{7}{2})^2-\frac{49}{4}-8 \\ y=(x-\frac{7}{2})^2-\frac{81}{4} \end{gathered}[/tex]The vertex of the function will be (7/2, -81/4)
The domain are the independent values of the function for which it exists. The domain of the given quadratic function exists on all real number that is:
[tex]Domain:(-\infty,\infty)[/tex]The range of the function are the dependent value for which it exist. For the given function, the range is given as:
[tex]Range:[-\frac{81}{4},\infty)[/tex]There are 33.8 fluid ounces in a liter. There are 128 fluid ounces in a gallon. How many litersthere are roughly in a gallon?to. 2b. 3C. 4d. 5Is your estimate greater or less than the exact number of liters in a gallon? Explainhow do you know.
Answer
Option C is correct.
There are roughly 4 liters in 1 gallon
And the estimate (4 liters in 1 gallon) is greaster then the exact number of liters in a gallon (3.79 liters in 1 gallon).
Explanation
We are given some parameters
33.8 fluid ounces = 1 liter
128 fluid ounces = 1 gallon
We are then told to find the amount of liters that are roughly in a gallon.
To do this, we will put the parameters that are equivalent as fractions on each other
[tex]\begin{gathered} \frac{33.8\text{ fluid ounces}}{1\text{ liter}}=1 \\ \frac{128\text{ fluid ounces}}{1\text{ gallon}}=1 \end{gathered}[/tex]We can write the first relation as an inverse and we will still have the same thing
[tex]\begin{gathered} \frac{1\text{ liter}}{33.8\text{ fluid ounces}}=1 \\ \frac{128\text{ fluid ounces}}{1\text{ gallon}}=1 \\ \text{ Since, 1 }\times1=1 \\ We\text{ can find the relation betw}een\text{ liter and gallon by saying} \\ \frac{1\text{ liter}}{33.8\text{ fluid ounces}}\times\frac{128\text{ fluid ounces}}{1\text{ gallon}} \\ \frac{128}{33.8}\frac{\text{liter}}{\text{gallon}} \\ =\frac{3.79\text{ liters}}{1\text{ gallon}} \end{gathered}[/tex]3.79 liters = 1 gallon
A right approximation will be that
1 gallon = 4 liters
We can then see that the estimate is greater than the exact number of liters in a gallon.
Hope this Helps!!!
List all numbers from the given set that area. natural numbersb. whole numbersd. rational numberse. irrational numbersc. integersf. real numbers{0.1. VT6.0. -2. 15. -3, 98. }a natural numbers =(Use a comma to separate answers as needed. Do not simplify.)b. whole numbers =(Use a comma to separate answers as needed. Do not simplify.)c. integers =(Use a comma to separate answers as needed. Do not simplify)d. rational numbers =(Use a comma to separate answers as needed. Do not simplify.)e irrational numbers =(Use a comma to separate answers as needed. Do not simplify.)f. real numbers =(Use a comma to separate answers as needed. Do not simplify.)
Given (12 ,7)and (X,-8) find all x such that the distance between these two points is 17 separate multiple answers with a comma
X=20
Explanationthe distance between 2 points is given by
[tex]\begin{gathered} for \\ P1(x_1,y_1) \\ P2(x_2y_2) \\ d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2} \end{gathered}[/tex]so
Step 1
a)given
[tex]\begin{gathered} P1(12,7) \\ P2(x,-8) \\ d=17 \end{gathered}[/tex]b) now, replace in the formula and solve for x
[tex]\begin{gathered} d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2} \\ 17=\sqrt{(x-12)^2+(-8-7)^2} \\ 17=\sqrt{(x-12)^2+(-15)^2} \\ raise\text{ both sides to power 2} \\ 17^2=(\sqrt{(x-12)^2+(-15)^2})^2 \\ 289=(x-12)^2+225 \\ subtract\text{ 225 in both sides} \\ 289-225=(x-12)^2+225-225 \\ 64=(x-12)^2 \\ square\text{ root in both sides} \\ \sqrt{64}=\sqrt{(x-12)^2} \\ 8=x-12 \\ add\text{ 12 in both sides} \\ 8=x-12 \\ 8+12=x-12+12 \\ 20=x \end{gathered}[/tex]therefore, the answer is
X=20
I hope this helps you
The figure below is a net for a right rectangular prism. Its surface area is 396 cm2 andthe area of some of the faces are filled in below. Find the area of the missing faces,and the missing dimension.
hello
to solve this question, let's add up all the areas from the sides given and equate it to the total area of the prism. Then we can also denote the side with the missing area as x
[tex]\begin{gathered} 396=42+72+42+72+x+x \\ 396=228+2x \\ 2x=396-228 \\ 2x=168 \\ \text{divide both sides by the coefficient of x} \\ \frac{2x}{2}=\frac{168}{2} \\ x=84 \end{gathered}[/tex]now we have established the area of the missing sides as 84cm^2
but then from careful observation, the figure with the missing side have a shape of a rectangle and we can use the formula of area of a rectangle to find the missing side.
[tex]\begin{gathered} a=l\times w \\ a=84\operatorname{cm}^2 \\ l=? \\ w=7\operatorname{cm} \\ 84=l\times7 \\ 84=7l \\ \frac{84}{7}=\frac{7l}{7} \\ l=12\operatorname{cm} \end{gathered}[/tex]from the calculations above, the missing side is equal to 12cm
how long will it take for the population to get to 2552 alligators?
we have the equation
[tex]P(t)=319(2)^{(\frac{t}{3})}[/tex]For P(t)=2,552
substitute in the given equation
[tex]2,552=319(2)^{(\frac{t}{3})}[/tex]solve for t
[tex]\begin{gathered} 2,552=319(2)^{(\frac{t}{3})} \\ \frac{2,552}{319}=(2)^{(\frac{t}{3})} \end{gathered}[/tex]Apply log both sides
[tex]\begin{gathered} \log \lbrack\frac{2,552}{319}\rbrack=\log \lbrack(2)^{(\frac{t}{3})}\rbrack \\ \log \lbrack\frac{2,552}{319}\rbrack=\frac{t}{3}\cdot\log (2) \end{gathered}[/tex]t=9 yearsthe answer is 9 years from the time of introductionRuth used a spinner to perform 10 to the probably of having the children whyes • Is Ruth's estimated probably representative of the theoretical probaby of having the children were? • Provide the estimated probability from this on and the theoretical probably of having them Respond in the space provide
Keshawn, this is the solution to part B:
P (blue) = 25% = 1/4
P (brown) = 75% = 3/4
If Ruth performs 10 trials, the theoretical probability would be:
P (blue) = 25% = 2.5/10
P (brown) = 75% = 7.5/10
Upon saying that, the outcome of 1 of having three children with blue eyes isn't a theoretical probability, it is a experimental probability.
Finally, the theoretical probability of having three children with blue eyes is:
P (3 chlildren with blue eyes) = 1/4 * 1/4 * 1/4 = 1/64
10<=6-2x<14 solve the inequality
Having that
10 ≤ 6 - 2x < 14
It meets two statements:
10 ≤ 6 - 2x and 6 - 2x < 14
We are solving each of them separately. We have to remember that we can add or substract any amount both sides of the inequalities and multiply or divide by a positive number both sides.
First statement: 10 ≤ 6 - 2xOn one hand, we want to solve:
10 ≤ 6 - 2x
then
10 ≤ 6 - 2x
↓ adding 2x both sides
10 + 2x ≤ 6
↓ substracting 10 both sides
2x ≤ 6 -10
↓ 6 - 10 = -4
2x ≤ -4
↓ dividing by 2 both sides
2x/2 ≤ -4/2
↓ -4/2 = -2
x ≤ -2
We have that x ≤ -2
Second statement: 6 - 2x < 14For the other hand, we want to solve
6 - 2x < 14
then
6 - 2x < 14
↓ adding 2x both sides
6 < 14 + 2x
↓ substracting 14 both sides
6 - 14 < 2x
↓ 6 - 14 = -8
-8 < 2x
↓ dividing by 2 both sides
-8/2 < 2x/2
↓ -8/2 = -4
-4 < x
We have that -4 < x
Therefore, joining both conclusions, we have that -4 < x and x ≤ -2, then
Answer: -4 < x ≤ -2First, let's look at the measures of the length and width of the wall the boys arepainting. The problem says that the wall is 7 feet wide and 6 feet tall. Frank paints14 square feet of the wall, and Ryan paints the rest.How can you draw one straight line on this grid to divide it into two sections toshow the part of the wall Frank paints and the part of the wall Ryan paints?
Let's draw the 7ft by 6ft wall that is being painted by Frank and Ryan.
If Frank paints 14 square feet of the wall, we can say that Frank painted two rows of 7ft wide. See illustration below.
The darker horizontal line is the straight line that divides the wall into two sections.
So, the orange part is the section where Frank paints and the blank (white) part is the part of the wall that Ryan paints.
Based on the function F(x) = 2x° +2x² - 4 and the graph of G(x) below, which of the following statements is true? TH O A. F(x) has 3 real roots x 70 G() O B. as x → = G(x) > 0 x → F(x) → O c. as x →-, F(x) — - O D. G(X) has 3 real roots
We could graph the function F:
[tex]F(x)=2x^3+2x^2-4[/tex]As follows:
As you can see,
[tex]\begin{gathered} as\text{ x}\to\infty,\text{ f(x)}\to\infty \\ as\text{ x}\to-\infty,\text{ f(x)}\to-\infty \end{gathered}[/tex]Therefore, the correct answer is C.