Solution:
Given the number below;
[tex]2586[/tex]To round uo, the rule is a follow;
If the last digit is less than 5, round the previous digit down. However, if it's 5 or more than you should round the previous digit up
To the nearest ten,
[tex]2590[/tex]To the nearest hundred,
[tex]2600[/tex]To the nearest thousand,
[tex]3000[/tex]17. A store charges 7% sales tax. Suppose an item in the store has a price of p dollars. Write a simplified expressionto represent the total cost of an item in the store.
The pice of the item is given as p
And the sales tax is 7% of the price
The total cost is equal to the price p plus the sales tax.
[tex]\text{Total cost = Price p + Sales tax }\rightarrow\text{equation 1}[/tex]Sales tax equals 7% of the price which is 7% of p.
[tex]\begin{gathered} \text{Sales tax = 7\% of p = }\frac{7}{100}\times p \\ \text{Sales tax = 0.07p} \end{gathered}[/tex]And price = p.
substituting into the equation 1, we have;
[tex]\begin{gathered} Total\text{ cost = Price + sales tax = p + 0.07p} \\ \text{Total cost = 1.07p dolars} \end{gathered}[/tex]Let C represent the total cost of an item.
Therefore, the simplified expression to represent the total cost of an item in the store is;
[tex]undefined[/tex]which value is a solution for 4x + 6 = 36
The given equation is expressed as
4x + 6 = 36
The first step is to subtract 6 from both sides of the equation. It becomes
4x + 6 - 6 = 36 - 6
4x = 30
x = 30/4
x = 7.5
Graph the parabola Y = X^2 + 6x +13 Play five points on a parabola the vertex two points to the left of the vertex and two points to the right of the vertex then click on the graph a function button
Given:
[tex]y=x^2+6x+13[/tex]To plot 5 points on the parabola:
The given equation can be written as,
[tex]\begin{gathered} y=x^2+6x++3^2-3^2+13 \\ y=(x+3)^2-9+13 \\ y=(x+3)^2+4 \end{gathered}[/tex]Therefore, the vertex of the parabola is (-3, 4).
Put x=-2, we get y=5. So, the point is (-2, 5).
Put x=-1, we get y=8. So, the point is (-1, 8).
Put x=-4, we get y=5. So, the point is (-4, 5).
Put x=-5, we get y=8. So, the point is (-5, 8).
So, the graph is,
find the slope of the line through each pair of points (9, 3) , (19, -17)
The expression of the slope with given two points can be expresses as:
[tex]Slope=\frac{y_2-y_1}{x_2-x_1}[/tex]The givne points : (9,3) & (19, -17)
SUbstitute the values and simplify
[tex]\begin{gathered} \text{ Slope=}\frac{19-9}{-17-3} \\ \text{ Slope=}\frac{10}{-20} \\ \text{ Slope=}\frac{-1}{2} \end{gathered}[/tex]Answer : Slope = -1/2
A farmer owns a total of 10 acres of land. The land is separated into 6 3/7 equally sized sections. How many acres are in each section?Write your answer as a mixed number in simplest form.
We need to divide 10 acres of land by 6 3/7 sections; therefore, if x is the number we are looking for
[tex]x=\frac{10}{6\text{ }\frac{3}{7}}=\frac{10}{6+\frac{3}{7}}=\frac{10}{\frac{45}{7}}=\frac{70}{45}=\frac{14}{9}=1+\frac{5}{9}=1\text{ }\frac{5}{9}[/tex]Thus, the answer is 1 5/9 acres.over a two hour time period a snail moved 50 inches how far is this in yards . write your answers as a whole number or a mixed number in simplest form
the distance is 50 inch
now we convert it into the yards
we know that
1 inch = 0.0277 yards
so in 50 inches
50 x 0.0277 = 1.38 yards or
[tex]1\frac{19}{50}[/tex]we can write the snail moved 1 yard. after rounding off 1.38
How would you write this in written form as an equation?
Explanation
We are given the parent function:
[tex]f(x)=\log_x[/tex]First, the horizontal shift 6 spaces to the left follows the rule:
[tex]f(x)\to f(x+6)[/tex]Next, the vertical shift 2 spaces down follows the rule:
[tex]\begin{gathered} f(x)\to f(x)-2 \\ f(x+6)\to f(x+6)-2 \end{gathered}[/tex]Finally, the reflection over y = k can be represented as:
[tex]\begin{gathered} Let\text{ }g(x)\text{ }be\text{ }the\text{ }combined\text{ }function \\ g(x)=2k+2-f(x+6) \\ \therefore g(x)=2k+2-log(x+6) \end{gathered}[/tex]Suppose k = 2, the graph becomes:
The red curve is the reflected curve.
Hence, the answer is:
[tex]\begin{equation*} g(x)=2k+2-log(x+6) \end{equation*}[/tex]what is th2 midpoint or the line segment with endpoints (3.2,2.5) and (1.6-4.5)?
We have to use the midpoint formula
[tex]M=(\frac{x_1+x_2}{2},\frac{y_1+y_2}{2})[/tex]Let's replace the given points
[tex]\begin{gathered} M=(\frac{3.2+1.6}{2},\frac{2.5-4.5}{2}) \\ M=(\frac{4.8}{2},\frac{-2}{2}) \\ M=(2.4,-1) \end{gathered}[/tex]Hence, the midpoint between (3.2, 2.5) and (1.6, -4.5) is (2.4, -1).based in this relationship, which could be the correlation cofficient?
The correlation coefficient "r" of a group of paired data (x,y) is a number that measures how much the data follows a linear model. This number has the following property:
[tex]-1\le r\le1[/tex]This means that it can only take values between -1 and 1, therefore options A, and D is not possible. When r = 1, this is a total positive linear correlation, and when r = -1 this is a total negative linear correlation. Positive linear correlation means that the data follow a linear model with a positive slope, that is the values of "y" increase in the positive direction as the values of "x" increase.
In this case, the altitude is the independent variable, therefore is analogous to "x", and the temperature is the dependent variable, therefore analogous to "y".
We see that as the values of "x" increase, the values of "y" decrease, therefore is a negative linear correlation therefore "r" must be smaller than zero. Therefore the only possible answer is -0.99
Suppose Aldo places $2000 in an account that pays 16% interest compounded each year.Assume that no withdrawals are made from the account.Follow the instructions below. Do not do any rounding.(a) Find the amount in the account at the end of 1 year.$(b) Find the amount in the account at the end of 2 years.$
It is given that $2000 was placed in an account that pays 16% interest compounded each year.
The Compound Interest Formula is given as:
[tex]A=P(1+\frac{r}{n})^{nt}[/tex]Where P is the amount placed in the account, r is the interest rate, n is the number of times the interest is compounded in a year, and t is the time passed in years.
(a) It is required to find the amount after 1 year.
Substitute P=2000, r=16%=0.16, n=1, and t=1 into the equation:
[tex]\begin{gathered} A=2000(1+\frac{0.16}{1})^{1(1)} \\ \Rightarrow A=2000(1+0.16)^1=2000(1.16)=\$2320 \end{gathered}[/tex](b) It is required to find the amount after 2 years.
Substitute P=2000, r=16%=0.16, n=1, and t=2 into the equation:
[tex]\begin{gathered} A=2000(1+\frac{0.16}{1})^{1(2)} \\ \Rightarrow A=2000(1+0.16)^2=2000(1.16)^2=2000(1.3456)=\$2691.2 \end{gathered}[/tex]Answers:
(a) $2320
(b) $2691.2
1)Given the following data set, find the mean, median, mode, and midrange.5, 6, 7, 7, 7, 8, 9, 10
Given:
[tex]5,\text{ 6, 7, 7, 7, 8, 9 , 10}[/tex]mean of the dataset
The mean is the average of the dataset and can be found using the formula:
[tex]mean\text{ = }\frac{Sum\text{ of the numbers}}{Total\text{ number of numbers}}[/tex]Substituting the given values:
[tex]\begin{gathered} mean\text{ = }\frac{5\text{ + 6 + 7 + 7 + 7 +8 + 9 + 10}}{8} \\ =\text{ }\frac{59}{8} \\ =7.375 \end{gathered}[/tex]Answer:
Mean = 7.375
Median of the dataset
The median is the value that lies at the center.
First, we arrange the data in ascending order
5, 6, 7, 7, 7, 8, 9, 10
Next, we find the value at the center
[tex]\begin{gathered} Median\text{ = }\frac{7+7}{2} \\ =\frac{14}{2} \\ =\text{ 7} \end{gathered}[/tex]Answer:
Median =
Mode of the dataset
The mode is the value with the highest frequency
Mode = 7
Mid-range of the dataset
The mid-range can be calculated using the formula:
[tex]Mid-range\text{ = }\frac{Max(x)\text{ + Min\lparen x\rparen}}{2}[/tex]Substituting the given values:
[tex]\begin{gathered} Mid-range\text{ = }\frac{5\text{ + 10}}{2} \\ =\text{ }\frac{15}{2} \\ =\text{ 7.5} \end{gathered}[/tex]BackgroundLayoutThemeTransition2467In 1991 Mike Powell set a world record in the long jump, jumping8.95 meters. How many millimeters did he jump?A 0.895 millimetersB 895 millimetersC 89.5 millimetersD 8950 millimeters
We have that in one meter there are 1000 milimeters, then, converting 8.95 meters to milimeteres we have:
[tex](8.95)(1000)=8950[/tex]therefore, Mike Powell jumped 8950 milimeteres
Could I please get help with this math problem on finding which pairs are congruent and which pairs are not congruent.
Given,
The diagram of the triangle is shown in the question.
For first diagram,
[tex]\begin{gathered} AC=DE \\ \angle A=\angle E \\ \angle B=\angle F \\ \therefore\Delta ABC\cong\Delta\text{DEF} \end{gathered}[/tex]The triangles are congruent by Angle-angle-side (AAS) property.
For second diagram,
[tex]\begin{gathered} UW=XY \\ \angle U=\angle X \\ \angle W=\angle Y \\ \therefore\Delta UVW\cong\Delta\text{XYZ} \end{gathered}[/tex]The triangles are congruent by Angle-side-angle (ASA) property.
For third diagram,
[tex]\begin{gathered} GI=JK \\ GH=KL \\ IH=JL \\ \therefore\Delta GHI\cong\Delta\text{JKL} \end{gathered}[/tex]The triangles are congruent by Side-side-Side (SSS) property.
consider the quadratic function F(x)=x^2-6x-7the vertex is_______its largest x intercept is x= ________its y intercept is y=_____
Given a equation:
[tex]\begin{gathered} f(x)=ax^2+bx+c \\ \text{the vertex, V(h,k) is:} \\ h=\frac{-b}{2a} \\ k=f(h) \end{gathered}[/tex]For:
[tex]\begin{gathered} F(x)=x^2-6x-7 \\ a=1 \\ b=-6 \\ c=-7 \\ h=\frac{-(-6)}{2(1)}=\frac{6}{2}=3 \\ k=F(h)=(3)^2-6(3)-7=9-18-7=-16 \end{gathered}[/tex]The vertex is (3,-16)
In order to find the x-intercepts, evaluate the function for F(x) = 0
[tex]\begin{gathered} F(x)=0 \\ x^2-6x-7=0 \\ \text{Factor:} \\ (x-7)(x+1)=0 \\ x=7 \\ or \\ x=-1 \end{gathered}[/tex]x-intercept: (7,0) and (-1,0)
In order to find the y-intercept, evaluate the function for x = 0:
[tex]\begin{gathered} F(0)=(0)^2-6(0)-7 \\ F(0)=-7 \end{gathered}[/tex]y-intercept: (0,-7)
how do I Write the explicit function for a geometric sequence with recursive functionare gn = gn-1 × 4; g1 = 2.
g1 =
(Simplify your answer. Use integers or fractions for any numbers in the expression.)
Given:
[tex]f(x)=4x+2[/tex][tex]y=4x+2[/tex][tex]x=4y+2[/tex][tex]4y=x-2[/tex][tex]y=\frac{x-2}{4}[/tex][tex]f^{-1}(x)=\frac{x-2}{4}[/tex]b)
Domain of f : Domain is the set of all real numbers.
c)
Let Red,blue and green lines represent the graph of f, f inverse and y=x
The length of a rectangle is 4 feet longer than twice the width. if the perimeter is 86 feet find the length and width of the rectangle
Let w be the width of the rectangle.
Let l be the length of the rectangle.
But l = w+4
Also,
[tex]\begin{gathered} Perimeter=2\mleft(l+w\mright) \\ 86=2((w+4)+w) \\ 86=2(2w+4) \\ 86=4w+8 \\ \text{Subtract 8 from both sides} \\ 86-8=4w+8-8 \\ 4w=78 \\ \text{Divide both sides by 4 to get} \\ \frac{4w}{4}=\frac{78}{4} \\ w=19.5ft \end{gathered}[/tex]Width = 19.5ft
Length = 19.5 + 4 = 23.5ft
Jo combines 4 bushels of wheat per minute. How many pounds of wheat does she harvest perhour?
Answer:
14,400 pounds of wheat per hour.
Explanation:
First, recall the standard conversion between bushels and pounds.
• Wheat has an assigned weight of 60 pounds.
Therefore:
[tex]1\text{ bushel of wheat=60 pounds}[/tex]Also:
[tex]\begin{gathered} 60\text{ minutes=1 hour} \\ \implies1\text{ minute=}\frac{1}{60}hour \end{gathered}[/tex]Therefore:
[tex]\begin{gathered} 4\frac{\text{bushels}}{\text{minute}}=\frac{4\times60}{\frac{1}{60}} \\ =4\times60\div\frac{1}{60} \\ =4\times60\times60 \\ =14,400\text{ pounds per hour} \end{gathered}[/tex]Thus, Jo harvests 14,400 pounds of wheat per hour.
If you are subtracting (3x2 + x) - (-2x2 + x), which of the following choices correctly adds the opposite of the second polynomial? (1 point) A A (3.x² + x) - (2x - x) B (3.rº + r) + (2x2 + x) C (3x2 + x) + (-2x2 – x)D (3.2? + x) + (2x2 – x) .
The given expression:
[tex](3x^2+x)-(-2x^2+x)[/tex]Open the brackets:
[tex]\begin{gathered} (3x^2+x)-(-2x^2+x) \\ (3x^2+x)-(-2x^2+x)=(3x^2+x)+2x^2-x \\ (3x^2+x)-(-2x^2+x)=(3x^2+x)+(2x^2-x) \end{gathered}[/tex]Answer: D)
[tex](3x^2+x)+(2x^2-x)[/tex]
how do I solve and what would be the answer
Given
The area of the rectangle is represented as,
[tex]A=14x^3-35x^2+42x[/tex]And, the length is represented as,
[tex]l=7x[/tex]To find the breadth of the rectangle.
Now,
The area of the rectangle is given by,
[tex]A=l\times b[/tex]Then,
[tex]b=\frac{A}{l}[/tex]Substitute the values of A and l in the above equation.
Then,
[tex]b=\frac{14x^3-35x^2+42x}{7x}[/tex]Since the common terrm in 14x^3-35x^2+42x is 7x.
Then,
[tex]\begin{gathered} b=\frac{7x(2x^2-5x+6)}{7x} \\ b=2x^2-5x+6 \end{gathered}[/tex]Hence, the breadth of the rectangle is 2x^2-5x+6.
i am stuck on this question, any help would be greatly appreciated The indicated line is the 3/5x+17 and is passing through the points -5, 15
We want to find a parallel line to y = (3/5)x + 17 passing through the point (-5,15)
Any two lines are parallel if they have the same slope.
Therefore, the line we are looking for must have slope 3/5
If the line passes through (-5,15), its slope s must be given by:
[tex]\begin{gathered} 15=\frac{3}{5}x+s \\ 15=\frac{3}{5}(-5)+s \\ 15=-3+s \\ s=18 \end{gathered}[/tex]Therefore, the line is given by:
[tex]y=\frac{3}{5}x+18[/tex]I got what I think is the answer pls help
Given the volume of a tiangular prism as shown below
[tex]V=\frac{1}{2}\times b\times h\times l[/tex]Where,
[tex]\begin{gathered} b=base \\ h=\text{height} \\ l=\text{length} \end{gathered}[/tex]Write out the parameters
[tex]\begin{gathered} b=2.1yd \\ h=1.2yd \\ l=5.5yd \end{gathered}[/tex]Substitute the values above in the volume formula
[tex]\begin{gathered} V=\frac{1}{2}\times2.1\times1.2\times5.5 \\ V=6.93yd^3 \end{gathered}[/tex]Hence, the volume of the triangular prism is 6.93yd³
number line scale. explain how and show to find 2 and oppisite of 2
Step 1
Draw a number line
Step 2
Since 0 is neither to the right nor to the left of 0, taking the opposite of 0 will give 0.
2 is a positive number, 2 is two units from 0 to the right.
Opposite of 2 is a negative number. -2 is the opposite of 2.
14/15 divided by 4/5 find the quotient
the equation can be writen like:
[tex]\frac{\frac{14}{15}}{\frac{4}{5}}[/tex]So we can operate the numerator of the first fraction by the denominator of the secon fraction, and the denominator of the fist equation by the numetator of the second fraction so:
[tex]\frac{14\cdot5}{15\cdot4}=\frac{70}{60}=\frac{7}{6}[/tex]Suppose that there are two types of tickets to a show: advance and same-day. The combined cost of one advance ticketand one same-day ticket is $65. For one performance, 25 advance tickets and 30 same-day tickets were sold. The totalamount paid for the tickets was $1750. What was the price of each kind of ticket?Advance ticket: s[]Same-day ticket: s[]
Let's call a the price of advance tickets, and s the price of same-day tickets.
The combined price of one and one is $65. Then, we can establish the following equation:
[tex]a+s=65[/tex]When 25 advance tickets and 30 same-day tickets were sold, the total amount paid for the tickets was $1750. Then, the sum of the total amount of money paid for advanced tickets (25a, the number of tickets paid multiplied by their price), and the total amount of money paid for the same-day tickets (30s, following the same logic), should add up to $1750. Representing that in an equation:
[tex]25a+30s=1750[/tex]Now we have a system of two equations and two unknowns (the price for each kind of ticket).
We can solve the system by using the substitution method.
We can isolate one of the variables from the first equation, and then replace the expression on the second equation. Solving for s in the first equation:
[tex]s=65-a[/tex]Now, we can replace that expression in the second equation instead of s:
[tex]25a+30\cdot(65-a)=1750[/tex]Now we have one equation with only one unknown. We can easily solve now the value of a:
[tex]\begin{gathered} 25a+30\cdot65-30a=1750 \\ 25a-30a=1750-30\cdot65 \\ -5a=1750-1950 \\ a=\frac{-200}{-5} \\ a=40 \end{gathered}[/tex]Then, the price of the advance ticket is $40.
Recalling that the combined price of one ticket of each class is $65:
[tex]a+s=65[/tex]Replacing the price of the advance ticket and solving:
[tex]\begin{gathered} 40+s=65 \\ s=65-40 \\ s=25 \end{gathered}[/tex]The price of the same-day tickets is $25
a student spend 3/7 of an hour each evening reading a book about biplanes if it took the student 9 Innings to finish the book how many hours in all did the students spend reading
Given data:
The total number of evening is e=9.
The fraction of hour in the eveninng is 3/7.
The total numbers of hour is,
[tex]\begin{gathered} t=9(\frac{3}{7}) \\ =\frac{27}{7} \\ =3\frac{6}{7} \end{gathered}[/tex]Thus, B) option is correct.
The value on decreasing of 15% from $ 1200 is equalto
SOLUTION
The original value given is
[tex]\text{ \$1200}[/tex]15% of the value give is
[tex]\begin{gathered} 15\text{ \% of 1200} \\ \end{gathered}[/tex]Since percentage means out of 100, then we have
[tex]\begin{gathered} \frac{15}{100}\times1200 \\ \text{Then} \\ =15\times12 \\ =180 \end{gathered}[/tex]Hence the decreasing value will be $180
Since the value is decreasing we have,
[tex]\begin{gathered} 1200-180 \\ =1020 \end{gathered}[/tex]Therefore
The decreasing of 15% from $1200 is $1020
Answer: $1020
The Cooking Club made some pies to sell ata basketball game to raise money for thenew math books. The cafeteria contributedfour pies to the sale. Each pie was then cutinto five pieces and sold. There were a totalof 60 pieces to sell. How many pies did theclub make?
SOLUTION
We know that the cooking club made pies to sell, but we don't know how many pies the cooking club made. So, let the number of pies the cooking club made be x.
Now the cafeteria contributed 4 pies that were cut into 5 pieces and sold. So the cafeteria contributed
[tex]4\text{ pies }\times5\text{ pieces = 20 pieces }[/tex]The cafeteria contributed 20 pieces.
Also we were told that a total of 60 pieces were sold. So what the club sold should be 60 pieces in total minus what the cafeteria sold.
So we have
[tex]60-20=40\text{ pieces }[/tex]The club sold 40 pieces.
Now remember that a pie is cut into 5 pieces, so this means that 40 pieces should make
[tex]\frac{40}{5}=8\text{ pies}[/tex]Hence the club made 8 pies
Directions: Determine whether each relation is a function. Explain your answer.D.(-1,10),(-2,13),(-3,16)E.(2,0),(2,-1),(3,-4)F. (33,10),(35,8),(36,10)
A set of pair of points satisfies the condition to be a function if one x-value does not have more than one y-value.
In Table D:
One x-value does not have more than one y-value.
Therefore, it is a function.
In Table E:
The x-value 2 has two y-values, 0 and -1.
Therefore, it is not a function.
In Table F:
One x-value does not have more than one y-value.
Therefore, it is a function.
Consider the following function.f(x) = cos 9x2 Find the derivative of the function.
The given function is:
[tex]f(x)=\cos(\frac{9x}{2})[/tex]It is required to find the derivative of the function and then use it to determine if the function is strictly monotonic, and hence has an inverse.
First, find the derivative of the function:
[tex]\begin{gathered} f(x)=\cos(\frac{9x}{2}) \\ Take\text{ derivative of both sides:} \\ f^{\prime}(x)=\frac{d}{dx}\cos(\frac{9x}{2}) \\ Using\text{ the chain rule }f^{\prime}(g(x))=\frac{d}{df}(f)\times\frac{d}{dx}(g(x))\text{, the derivative is:} \\ f^{\prime}(x)=-\sin(\frac{9x}{2})\times\frac{d}{dx}(\frac{9x}{2})=-\frac{9}{2}\sin(\frac{9x}{2}) \\ \Rightarrow f^{\prime}(x)=-\frac{9}{2}\sin(\frac{9x}{2}) \end{gathered}[/tex]Notice that the derivative of the function is a trigonometric function that is sinusoidal (alternates in values from negative to positive).
A function is strictly monotonic if its derivative is strictly positive or strictly negative over its entire domain.
Hence, the given function is not strictly monotonic and therefore does not have an inverse.
Answers:
The derivative of the function is:
[tex]f^{\prime}(x)=-\frac{9}{2}\sin(\frac{9x}{2})[/tex]The given function is not strictly monotonic and therefore does not have an inverse.