The given expression is,
[tex]\frac{2047}{41}[/tex]On solving, we have,
[tex]\frac{2047}{41}=49\frac{38}{41}=49.93[/tex]Thus, 2,047÷41=49.93.
Jessica is deciding on her schedule for next semester. She must take each of the following classes: English 101, Spanish 102, Biology 102, andCollege Algebra. If there are 15 sections of English 101,9 sections of Spanish 102, 13 sections of Biology 102, and 15 sections of College Algebra,how many different possible schedules arethere for Jessica to choose from? Assume there are no time conflicts between the different classes.Keypad
Jessica must take four classes: English, Spanish, Biology, and College Algebra.
There are:
15 sections of English
9 sections of Spanish
13 sections of Biology
15 sections of College Algebra.
She has 15 possible choices for English class. Once selected, she has 9 choices for Spanish class.
There is a total of 15*9 = 135 possible schedules for both subjects.
When we combine this with the rest of the classes, we find a total of:
15*9*13*15 = 26,325 possible schedules, assuming there are no time conflicts between them.
Answer: 26,325
Evaluate an exponential function that models a real world problem
Answer:
• Initial value: $26,000.
,• Value after 12 years: $1,319
Explanation:
The value of a car model that is t years old is given by the function:
[tex]v(t)=26,000(0.78)^t[/tex](a)The Initial Value
At the initial point of purchase, the value of t=0.
[tex]\begin{gathered} v(0)=26,000(0.78)^0 \\ =26000\times1 \\ =\$26,000 \end{gathered}[/tex]The initial value is $26,000.
(b)Value after 12 years
When t=12:
[tex]\begin{gathered} v(12)=26,000(0.78)^{12} \\ =1318.6 \\ =\$1,319 \end{gathered}[/tex]The value of the car after 12 years is $1,319 (correct to the nearest dollar).
what is the size of rectungle 2x2x2
Perimeter: 8 u
Area: 4 u^2
Volume: 8 u^3
Explanation:
u = unit (cm / m etc...)
side = 2 u
Formula for a rectangle:
Perimiter : 2*(side + side)
=> 2 * ( 2 + 2) = 8 u
Area: side * side
=> 2 * 2 = 4 u^2
Volume: Area * Height
=> 2 * 4 u^2 = 8 u^2
a school ordered three large boxes of board markers after giving 15 markers to each of three teachers there were ninety X the diagram represents the situation how many markers were original in the
Determine the value of x.
[tex]\begin{gathered} x-15+x-15+x-15=90 \\ 3x=90+45 \\ x=\frac{135}{3} \\ =45 \end{gathered}[/tex]So there are 45 markers originally in each box.
Janelle alternates between running and walking. She begins by walking for a short period, and then runsfor the same amount of time. She takes a break before beginning to walk again. Consider the four graphsbelow. Which graph best represents the given situation?
the answer is letter C
letter C best represents a situation in which Janelle starts walking and then running.
We can know this by the slope of the lines.
Jessica bought a house at auction for $82,500. The auction company charges a 15% premium on the final bid. how much will jessica pay for the house
First, we need to find the 15% of $82,500 as:
[tex]82,500\cdot15\text{ \% = 82,500 }\cdot\frac{15}{100}=12,375[/tex]It means that Jessica will pay $82,500 for the house plus $12,375 to the auction company. So, in total, Jesica will pay for the house:
$82,500 + $12,375 = $94,875
Answer: $94.875
answer.The number of cities in a region over time is represented by the function C(=) = 2.9(1.05). The approximate number of people per city isrepresented by the function P(t) = (1.05)35 +5.Which function best describes T(*), the approximate population in the region?OA T(I) = (3.045)* + (1.05)35 +5OB. T(1) = (6.09)45+5OC. T() = 2.9(1.05)45+5OD. Т(1) = 2.9(1.05)352 +55
Given:
[tex]\begin{gathered} \text{Number of cities: }C(x)=2.9(1.05)^x \\ \\ \text{Number of people per city: P}(x)=(1.05)^{3x+5} \end{gathered}[/tex]Let's solve for T(x) which represents the approximate population in the region.
To find the approximate population in the region, apply the formula:
[tex]T(x)=C(x)\ast P(x)[/tex]Thus, we have:
[tex]T(x)=2.9(1.05)^x\ast(1.05)^{3x+5}^{}[/tex]Let's solve the equation for T(x).
Thus, we have:
[tex]\begin{gathered} T(x)=2.9((1.05)^{3x+5}(1.05)^x) \\ \\ Apply\text{ power rule:} \\ T(x)=2.9(1.05)^{3x+5+x^{}_{}} \\ \\ T(x)=2.9(1.05)^{3x+x+5} \\ \\ T(x)=2.9(1.05)^{4x+5} \end{gathered}[/tex]Therefore, the function that best describes the approximate population in the region is:
[tex]T(x)=2.9(1.05)^{4x+5}[/tex]ANSWER:
C
[tex]T(x)=2.9(1.05)^{4x+5}[/tex]Find all the roots of y = x4 + 7x3 + 25x2 - 11x – 150
Given the equation :
[tex]y=x^4+7x^3+25x^2-11x-150[/tex]to find the roots of he function , y = 0
so,
[tex]x^4+7x^3+25x^2-11x-150=0[/tex]the factors of 150 are;
1 x 150 , 2 x 75 , 3 x 50 , 5 x 30 ,
We will check which number give y = 0
so, when x = 1 , y = -128
When x = -1 , y = -120
when x = 2 , y = 0
So, x = 2 is one of the roots
so ( x - 2 ) is one of the factors of the given equation :
Make a long division to find the other roots:
so,
[tex]\frac{x^4+7x^3+25x^2-11x-150}{x-2}=x^3+9x^2+43x+75[/tex]See the following image:
Now , we will repeat the steps for the result
the factors of 75
1 x 75 , 3 x 25 , 5 x 5
We will check which number give y = 0
when x = 1 , y = 128
when x = -1 , y = 40
When x = 3 , y = 312
when x = -3 , y = 0
so, x = -3 is another root
So, ( x + 3 ) is one of the factors
so, make a long division again to find the other roots:
[tex]\frac{x^3+9x^2+43x+75}{x+3}=x^2+6x+25[/tex]See the following image :
Now the last function :
[tex]x^2+6x+25=0[/tex]a = 1 , b = 6 , c = 25
[tex]D=\sqrt[]{b^2-4\cdot a\cdot c}=\sqrt[]{36-4\cdot1\cdot25}=\sqrt[]{36-100}=\sqrt[]{-64}=i\sqrt[]{64}=\pm8i[/tex]which mean the last equation has no real roots
So,
the roots of the given equation is just two roots
So, the answer is the roots of the given eaution is x = 2 and x = -3
DiaporamGiven the diagram below and the following statements. GliProve that mZHIW90".HEZGIW and ZHW are supplementaryReasonmZGIH+mZHIW-180°ReasonEnter the unknown statements and reasons to complete theflow chart proof. You can click the Organize button at anytime to have the tutor automatically organize the nodes inthe flow chart .StatementSubtraction Property ofConclusion
Step 1
Perpendicular lines are lines that meet at right-angles or 90°
Step 2
First statement: Definition of right angles
Second statement:
2x-5y= -19
-3x+y=9
solve by substitution
Answer: (-2,3)
Step-by-step explanation:
2x-5y=-19 (1)
-3x+y=9 (2)
2x-5y=-19 (3)
y=3x+9 (4)
2x-5(3x+9)=-19
2x-15x-45=-19
-13x=-19+45
-13x=26
Divide both parts of the equation by -13:
x=-2
Substitute the value of x=-2 into equation (4):
y=3(-2)+9
y=-6+9
y=3
Thus, (-2,3)
I am doing a homework assignment but i don’t quite understand this one may it be explained step by step?
Part A: Use the graph to identify the zeros of the polynomial.
As it is said in the introduction the graph crosses 3 times the x -axis and touched it at (2,0).
Values of x for which the function is zero can be identified by knowing the x-coordinate of these points:
[tex]x=-4[/tex][tex]x=2[/tex]And the following two that are approximate values taken from the graph:
[tex]x\approx-1.6[/tex][tex]x\approx3.6[/tex]Part B: Use the behaivor of the graph to explain whether the dregree of the polinomial is even or odd.
The graph the graph corresponds to an odd function because has no symmetry abopur the y-axis and when the value of x get smaller the values of y also. To the left from a certain point lower values are always obtained and to the right from a certain point higher values are always obtained.
In Millersburg, the use of landlines has been declining at a rate of 10% every year. If there are 42,000 landlines this year, how many will there be in 7 years?If necessary, round your answer to the nearest whole number.
To calculate how many landlines will be used in 7 years you have to apply the exponential decay
[tex]y=a(1-r)^x[/tex]Where
a is the initial value
r is the decay rate (this value is given as a percentage, you have to use it expressed as a decimal)
x is the time interval that has passed
We know that there are 42000 landlines this year
The declining rate is 10% → expressed as a decimal value r=0.1
The time-lapse is 7 years
[tex]\begin{gathered} y=42000(1-0.1)^7 \\ y=20088.47 \end{gathered}[/tex]In 7 years there will be 20088.47 landlines
find a slope of the line that passes through (8,2) and (6,3)
EXPLANATION
Given the dots:
(x1,y1)=(8,2) and (x2,y2)=(6,3)
The slope equation is:
[tex]\text{Slope = }\frac{(y_2-y_1)}{(x_2-x_1)}[/tex]Replacing the ordered pairs in the slope equation will give us:
[tex]\text{Slope = }\frac{(3-2)}{(6-8)}=\frac{1}{-2}=-\frac{1}{2}[/tex]The slope of the line is -1/2.
nWhich graph shows the solution set of the compound inequality 1.5x-1 > 6.5 or 7X+3 <-25?-1010O-1050510-10-5510+-105010Mark this and returnSave and ExitNextSubmit
Solving the first inequality >>>
[tex]\begin{gathered} 1.5x-1>6.5 \\ 1.5x>6.5+1 \\ 1.5x>7.5 \\ x>5 \end{gathered}[/tex]Solving the second inequality >>>>
[tex]\begin{gathered} 7x+3<-25 \\ 7x<-25-3 \\ 7x<-28 \\ x<-\frac{28}{7} \\ x<-4 \end{gathered}[/tex]So, the solution set will be all numbers less than -4 and all numbers greater than 5.
We will have open circle at -4 and 5 and arrows to both sides.
From answer choices, second option is the right graph.
All questions relate to the equation y=9 x^2-36 x+37Got it.1. Which way does the parabola open? Your answerYour answerYour answer2. What is the minimum value of y?Your answer3. What is the maximum value of y?Your answer5. What is the axis of symmetry?7. What is the y-intercept?Your answer8. Rewrite the equation in vertex form.
Given the parabola:
[tex]y=9x^2-36x+37[/tex]Part 1
To determine the way the parabola opens, we consider the coefficient of x².
• If the coefficient is positive, it opens downwards.
,• If the coefficient is negative, it opens upwards.
In this case, the coefficient of x²=9 (Positive).
The parabola opens downwards.
Part 2
The minimum value of the parabola occurs at the line of symmetry.
First, we find the equation of the line of symmetry.
[tex]\begin{gathered} x=-\frac{b}{2a};a=9,b=-36,c=37 \\ \therefore x=-\frac{(-36)}{2\times9} \\ x=2 \end{gathered}[/tex]Find the value of y when x=2.
[tex]\begin{gathered} y=9x^2-36x+37 \\ y=9(2)^2-36(2)+37 \\ =36-72+37 \\ Min\text{imum value of y=1} \end{gathered}[/tex]Part 3
Since the graph has a minimum value, the maximum value of y will be ∞.
Part 5
As obtained in part 2 above, the axis of symmetry is:
[tex]x=2[/tex]Part 6
The vertex is the coordinate of the minimum point.
At the minimum point, when x=2, y=1.
Therefore, the vertex is (2,1).
Part 7
The y-intercept is the value of y when x=0.
[tex]\begin{gathered} y=9x^2-36x+37 \\ y=9(0)^2-36(0)+37 \\ y=37 \end{gathered}[/tex]The y-intercept is 37.
Part 8
We rewrite the equation in Vertex form below:
[tex]\begin{gathered} y=9x^2-36x+37 \\ y-37=9x^2-36x \\ y-37+36=9(x^2-4x+4) \\ y-1=9(x-2)^2 \\ y=9(x-2)^2+1 \end{gathered}[/tex]Hey I need help on this math problem ignore the lines across the answer choices it’s a glitch I can’t change it and the lines don’t mean that the answer choice is wrong
Solution:
Given:
Two box plots for city A and city B.
A box plot with its representations is shown:
From the box plot given:
For City A :
[tex]\begin{gathered} City\text{ A:} \\ Q_3=78 \\ Q_1=76 \\ Interquartile\text{ range \lparen IQR\rparen}=Q_3-Q_1 \\ IQR=78-76 \\ IQR=2 \end{gathered}[/tex]For City B :
[tex]\begin{gathered} City\text{ B:} \\ Q_3=78 \\ Q_1=68 \\ Interquartile\text{ range \lparen IQR\rparen}=Q_3-Q_1 \\ IQR=78-68 \\ IQR=10 \end{gathered}[/tex]From the IQR calculated, the correct answer is:
The interquartile range for city B is greater.
F(x)=2|x-1| Graph using transformations and describe the transformations of the parent function y =x^2.
[Please see that in the question should be a mistake regarding the parent function. It should be written y = |x| instead of y = x².]
To answer this question, we need to know that the below function is a transformation of the parent function, f(x) = |x|:
[tex]f(x)=2|x-1|[/tex]Describing the transformationsTo end up with the above function from the parent function, we need to follow the next steps:
1. Translate the function, y = |x| one unit to right. We can do this by subtracting one unit to the parent function as follows:
[tex]f(x)=|x-1|[/tex]We can see this graphically as follows:
The blue function is the first transformation of the parent function, f(x) = |x|.
2. The function has been dilated by a factor of 2 from the x-axis. That is, the function has been dilated by a factor of 2 vertically. Then, we have:
[tex]f(x)=2|x-1|[/tex]And now, we can see the transformation graphically as follows:
Therefore, the blue line is the graph representation of the function:
[tex]f(x)=2|x-1|[/tex]What is the volume of this sphere?
Use a ~ 3.14 and round your answer to the nearest hundredth.
Radius =3 m
cubic meters
Explanation
We are asked to get the volume of the sphere
The volume of a sphere is given by
[tex]\begin{gathered} V=\frac{4}{3}\pi r^3 \\ \\ where\text{ r = radius =3m} \\ \pi=3.14 \end{gathered}[/tex]The volume of the sphere will be
[tex]V=\frac{4}{3}\times3.14\times3^3=113.04m^3[/tex]Therefore, the volume of the sphere will be 113.04m³
A wildlife park manager is working on a request to expand the park. In a random selection during one week, 3 of every 5 cars have more than 3 people insideIf about 5,000 cars come to the park in a month, estimate how many cars that month would have more than 3 people inside.
Determine the ratio of cars that have more than 3 people.
[tex]\frac{3}{5}[/tex]Since in a month 5000 cars comes to park. Then cars with more than 3 people are,
[tex]\begin{gathered} \frac{3}{5}\cdot5000=3\cdot1000 \\ =3000 \end{gathered}[/tex]Answer: 3000
Which of the following sets number could not represent the three sides of a right triangle
Given 4 sets of three sides of a triangle
We will find Which of the following sets of numbers could not represent the three sides of a right triangle
First, for any right triangle, the sum of the square of the legs is equal to the square of the hypotenuse
The hypotenuse is the longest side of the triangle
We will check the options:
a) { 11, 60, 61}
[tex]11^2+60^2=121+3600=3721=61^2[/tex]So, option a represent a right triangle
b) {46, 60, 75 }
[tex]46^2+60^2=2116+3600=5716\ne75^2[/tex]So, option (b) does not represent a right triangle
No need to check the other options
So, the answer will be {46, 60, 75}
A book sold 33,400 coples in its first month of release. Suppose this represents 7.6% of the number of coples sold to date. How many coples have been sold todate?Round your answer to the nearest whole number.
The number sold in the first month is given as 33,400.
This number is 7.6 percent of the total copies sold till date. This means x copies have been sold till date, and x copies represents 100 percent.
Therefore, you would have the following proportion;
[tex]\begin{gathered} \frac{33400}{x}=\frac{7.6}{100} \\ \text{Cross multiply and you'll have;} \\ \frac{33400\times100}{7.6}=x \\ 439473.684210\ldots=x \\ x\approx439474\text{ (rounded to the nearest whole number)} \end{gathered}[/tex]The number of copies sold till date is 439,474 (rounded to the nearest whole number)
1. A taxi driver records the time required to complete various trips and the distance for each trip. time (minutes) The equation for the line of best fit is y=0.50x + 0.40. Which of the following statements BEST interprets the slope of the line of best file A. For every 0.50 minute increase in time, the distance increases by 1 mile. B. For every 1 minute increase in time, the distance increases by 0.50 miles. C. For every 0.54 ninute increase in time, the distance decreases by 1 mile. . D. For every 1 minute increase in time, the distance decreases by 0.50 miles.
Given
Equation
y = 0.5x + 0.4
Procedure
Slope = 0.5
Intercept = 0.4
B. For every 1 minute increase in time, the distance increases by 0.50 miles.
A local little league has a total of 70 players, of whom 80% are right-handed. How many right-handed players are there? There are right-handed players.
there are (0,80)(70)=56 right handed players
Refer to the table which summarizes the results of testing for a certain disease. A test subject is randomly selected and tested for the disease. What is the probability the subject has the disease given that the test result is negative. Round to three decimal places as needed.Positive Test ResultNegative Test ResultSubject has the disease879Subject does not have the disease27312
Answer: 0.021
First, we will find the total number of results by adding up all the subject results in the table:
[tex]87+9+27+312=435[/tex]Now, we know there are 435 total results. We are asked to find the probability that the subject has the disease given that the test result is negative.
Looking at the table, we can see that the number of subjects that has the disease despite having negative results is 9. We will then divide these results by the total number of subject results to find the probability being asked:
[tex]P=\frac{9}{435}=0.020689\approx0.021[/tex]With this, we know that the probability of the subject having the disease given the results is negative is 0.021.
Determine if the side lengths could form a triangle. Use an inequality to justify your answer.16 m, 21 m, 39 m
We can draw the following triangle
the triangle inequality state that
[tex]|a-b|where | | is the absolute value. In our case, if we apply this inequality we obtain[tex]|21-39|which gives[tex]\begin{gathered} |-18|since 21m is between 18m and 60m, the values 16m, 21mn and 39m can form a triangle.On which number line the location of point P represent the probability of an event that is likely, but not certain?
The straight line that best represents something probable but not certain is option D.
It shows a probability of approximately 80%.
Note: Figure is not drawn to scale.If h= 13 units and r= 4 units, then what is the approximate volume of the cone shown above?OA. 52 cubic unitsOB. 69.337 cubic unitsOC. 2087 cubic unitsOD. 225.337 cubic units
The volume of a right circular cone is computed as follows:
[tex]V=\pi r^2\frac{h}{3}[/tex]where r is the radius and h is the height of the cone.
Substituting with r = 4 units and h = 13 units, we get:
[tex]\begin{gathered} V=\pi4^2\frac{13}{3} \\ V=\pi16\frac{13}{3} \\ V=\frac{208}{3}\pi\approx69.33\pi \end{gathered}[/tex]See attached question answer in in terms of log and a fraction
Given:
[tex]\int_4^{\infty}\frac{1}{x^2+x}\text{ dx}[/tex]To find:
the integral
[tex]\begin{gathered} First,\text{ we will re-write the expression} \\ \frac{1}{x^2+x}\text{ = }\frac{1}{x^2(1\text{ + }\frac{1}{x})} \\ \\ let\text{ u = 1 + 1/x} \\ u\text{ = 1 + x}^{-1} \\ \frac{du}{dx\text{ }}\text{ = 0 + \lparen-1}x^{-1-1})\text{ = -1x}^{-2} \end{gathered}[/tex][tex]\begin{gathered} \frac{du}{dx}\text{ = -x}^{-2} \\ \\ du\text{ = -x}^{-2}dx \\ du\text{ = }\frac{dx}{-x^2} \\ \\ \int_4^{\infty}\frac{1}{x^2+x\text{ }}dx\text{ = }\int_4^{\infty}\frac{1}{x^2(1\text{ +}\frac{1}{x})}dx \\ \\ Substitute\text{ for u and du in the expression:} \\ \int_4^{\infty}\frac{1}{x^2(u)}dx\text{ = }\int_4^{\infty}\frac{dx}{-x^2(u)}=\int_4^{\infty}-\frac{du}{u} \\ \end{gathered}[/tex][tex]\begin{gathered} -\int_4^{\infty}\frac{du}{u}=-\int_4^{\infty}ln\text{ u \lparen differentiation rule\rparen} \\ \\ \int_4^{\infty}ln(1+\frac{1}{x})=\int_4^{\infty}ln(\frac{x+1}{x})=\int_4^{\infty}ln(x+1)\text{ - ln\lparen x\rparen} \\ \\ -\int_4^{\infty}ln(1+\frac{1}{x})=-\int_4^{\infty}ln(x+1)\text{ - ln\lparen x\rparen = }\int_4^{\infty}ln(x)\text{ - ln\lparen x+1\rparen} \\ \\ -\int_4^{\infty}ln(1+\frac{1}{x})=\text{ \lbrack\lparen}\lim_{x\to\infty}(ln(x)\text{ - ln\lparen x+1\rparen\rbrack- \lbrack lnx - ln\lparen x+1\rparen\rbrack}_{x=4} \\ \\ -\int_4^{\infty}ln(1+\frac{1}{x})=\text{ \lbrack}\frac{x}{x+1}\text{\rbrack}_{\infty}\text{ - ln\lbrack}\frac{x}{x+1}]_4 \\ \\ -\int_4^{\infty}ln(1+\frac{1}{x})=0\text{ - ln\lbrack}\frac{4}{4+1}] \\ \\ -\int_4^{\infty}ln(1+\frac{1}{x})=\text{ -ln\lbrack}\frac{4}{5}] \end{gathered}[/tex][tex]-\int_4^{\infty}ln(1+\frac{1}{x})\text{ = ln\lparen}\frac{5}{4})[/tex]Would you Please Solve it and explain little[tex]14(.5 + k) = - 14[/tex]
To solve the given equation, we first apply the distributive property on the left side.
So, we have:
[tex]\begin{gathered} 14(0.5+k)=-14 \\ 14\cdot0.5+14\cdot k=-14 \\ 7+14k=-14 \\ \text{ Subtract 7 from both sides of the equation} \\ 7-7+14k=-14-7 \\ 14k=-21 \\ \text{ Divide by 14 from both sides} \\ \frac{14k}{14}=-\frac{21}{14} \\ k=-\frac{21}{14} \end{gathered}[/tex]Finally, we simplify.
[tex]\begin{gathered} k=-\frac{3\cdot7}{2\cdot7} \\ $$\boldsymbol{k=-\frac{3}{2}}$$ \end{gathered}[/tex]Therefore, the solution of the given equation is -3/2.
I dont really get it or what it is asking
ANSWER
• A vertical plane that cuts through the top vertex, perpendicular to the base,: ,triangle
,• A horizontal plane, that cuts through the pyramid, parallel to the base:, ,square
,• A vertical plane that cuts through the base and two opposite lateral faces:, ,trapezoid
EXPLANATION
• A vertical plane that cuts through the top vertex, perpendicular to the base,: if we draw a rectangle perpendicular to the base that passes through the vertex,
Hence, the cross-sectional shape is a triangle.
• A horizontal plane, that cuts through the pyramid, parallel to the base:, if it is a plane parallel to the base, then it should have the same shape as the base,
Hence, the cross-sectional shape is a square.
• A vertical plane that cuts through the base and two opposite lateral faces:, again, we can draw this plane. The cross-sectional shape will have one pair of parallel sides and one pair of non-parallel sides,
Hence, the cross-sectional shape is a trapezoid.