We have an original annual original budget of $1475. For each month of the year, we have then:
[tex]m=\frac{1475}{12}\approx122.92[/tex]Thus, we have for each month, a monthly budget of $122.92 for spending on social media.
However, in December this budget was increased by 20%, then:
[tex]122.92\cdot\frac{20}{100}=24.58[/tex]Then the budget for the month of December is:
[tex]BD=122.92+24.58\Rightarrow BD=147.5[/tex]Can you help meSolve(2/9)³+13⁰
737/729
1) Let's solve that expression with two powers.
[tex]\begin{gathered} (\frac{2}{9})^3+13^0 \\ \text{Any power raised to 0 is =1} \\ (\frac{8}{729})+1 \\ \text{LCM 1 and 729}=729 \\ \frac{\square}{729} \\ \\ \text{Let's divide 729 by 729 and multiply by 8} \\ \frac{(\frac{729}{729\text{ }}=1\text{ }\times8)}{729} \\ \frac{8}{729} \\ \frac{\frac{729}{1}=\text{ 729 x 1}}{729}=\frac{729}{729} \\ \text{Hence,} \\ \frac{8}{729}+\frac{729}{729}=\frac{737}{729} \end{gathered}[/tex]2) So the answer to that expression, considering that any number raised to 0 is equal to 1 and taking the LCM (Least Common Multiple) to turn those fractions into one with the same denominator and then sum turns out to be 737/729
Read the following conjectures and decide if they are true or false: • Angles that are adjacent angles share a vertex. • All right angles are supplementary angles. • The square of all odd numbers is an odd number • The product of an even number and odd number is even Counterexamples:
1) Angles that are adjacent share a common vertex = True
Points to know about adjacent angles:
They have a side in common
They have a common vertex
They do not overlap
2) All right angles are supplementary angles = False
Right angles = 90 degrees (they are complementary)
3) The square of all odd numbers is an odd number = True
All odd numbers take the form 2n + 1 (notice the offshoot of 1)
The square of odd numbers will be :
(2n + 1) ² = 4n ² + 4n + 1 (this also has an offshoot of 1)
This means that both an odd number and its square are odd
4) The product of an even number and an odd number is even = True
Calculate the sum of interior angles of a 6 sided polygon
The sum of interior angles of a polygon can be calculated using the formula below.
[tex]\begin{gathered} S\text{ = }(n-2)\times180^0 \\ \text{Where; } \\ S\text{ = sum of interior angles of the polygon } \\ n\text{ = number of sides of the polygon} \end{gathered}[/tex]For the given question the polygon is 6 sided, so;
[tex]n\text{ = 6}[/tex]Substituting the value of n into the formula, we have;
[tex]\begin{gathered} S\text{ = (6-2)}\times180^0 \\ S\text{ = 4}\times180^0 \\ S=720^0 \end{gathered}[/tex]Therefore, the sum of interior angles of a 6 sided polygon is 720 degree
[tex]S=720^0[/tex]A door to playhouse is 50 inches tall.Which of the following is another measure eaqual to the height?A.4 ft 2 in.B.4 ft 1 in.C.4 ft 1/2 in.D.5 ft
Dereo, this is the solution:
All we need to do is to convert inches to feet, as follows:
Let's recall that:
12 inches = 1 feet
In consequence,
50 inches = 50/12 feet
50 inches = 4 feet + 2 inches
The correct answer is A.
Find the equation for the line with the given properties. Sketch the graph of the line. Passes through (2, -5) and (7,3)
We have to find the equation of the line that passes through points (2,-5) and (7,3).
We can start by calculating the slope m as:
[tex]m=\frac{y_2-y_1}{x_2-x_1}=\frac{3-(-5)}{7-2}=\frac{3+5}{5}=\frac{8}{5}[/tex]With one point and the slope, we can write the line equation in slope-point form and then rearrange it:
[tex]\begin{gathered} y-y_2=m(x-x_2) \\ y-3=\frac{8}{5}(x-7) \\ y-3=\frac{8}{5}x-\frac{56}{5} \\ y=\frac{8}{5}x-\frac{56}{5}+3\cdot\frac{5}{5} \\ y=\frac{8}{5}x-\frac{56}{5}+\frac{15}{5} \\ 5y=8x-56+15 \\ 5y=8x-41 \\ -8x+5y+41=0 \\ 8x-5y-41=0 \end{gathered}[/tex]The equation in general form is 8x-5y-41 = 0.
We can sketch it as:
Find two points on the line to graph the function Any lines orCurves will be drawn once all required points are plotted
ANSWER:
A: (4, 9)
B: (-1, -3)
STEP-BY-STEP EXPLANATION:
We have the following function:
[tex]q(x)=4x-\frac{(3+8x)}{5}[/tex]We determine the two points when x = 4 and when x = -1, like this:
[tex]\begin{gathered} q(4)=4\cdot4-\frac{\left(3+8\cdot4\right)}{5}\: \\ \\ q(4)=16-\frac{3+32}{5}=16-7 \\ \\ q(4)=9 \\ \\ A=(4,9) \\ \\ q(-1)=4\cdot\left(-1\right)-\frac{\left(3+8\cdot(-1)\right)}{5}\: \\ \\ q(-1)=-4-\frac{3-8}{5} \\ \\ q(-1)=-4-(-1)=-4+1 \\ \\ q(-1)=-3 \\ \\ B=(-1,-3) \end{gathered}[/tex]Therefore point A is (4, 9) and point B is (-1, -3)
find the measure of all labeled angles in the diagram
Answer:
∠1 = 127°
∠2 = 53°
∠3 = 127°
∠4 = 37°
∠5 = 53°
∠6 = 90°
∠7 = 37°
∠8 = 143°
∠9 = 37°
∠10 = 143°
Explanation:
If two angles form a straight line, they add to 180°, so ∠1, ∠2, and ∠3 can be calculated as:
∠1 = 180 - 53 = 127°
∠2 = 180 - ∠1 = 180 - 127 = 53°
∠3 = 180 - 53 = 127°
Then, ∠5 is corresponding to 53° because they are in the same relative position. It means that these angles have the same measure, so:
∠5 = 53°
On the other hand, ∠6 is opposite to the right angle, so it has the same measure, then:
∠6 = 90°
∠4, ∠5, and ∠6, form a straight line, so:
∠4 = 180 - ∠5 - ∠6
∠4 = 180 - 53 - 90
∠4 = 37°
Finally, the sum of the interior angles of a triangle is also 180°, so the measure ∠7 will be equal to:
∠7 = 180 - ∠2 - ∠6
∠7 = 180 - 53 - 90
∠7 = 37°
So, the measures of ∠8, ∠9, and ∠10 will be equal to:
∠8 = 180 - ∠7 = 180 - 37 = 143°
∠9 = 180 - ∠8 = 180 - 143 = 37°
∠10 = 180 - ∠7 = 180 - 37 = 143°
Therefore, the answers are:
∠1 = 127°
∠2 = 53°
∠3 = 127°
∠4 = 37°
∠5 = 53°
∠6 = 90°
∠7 = 37°
∠8 = 143°
∠9 = 37°
∠10 = 143°
Solve the compound an equality. Write the solution in interval notation.
Step 1: Write the two inequalities equations
[tex]4u\text{ + 1 }\leq\text{ -3 -2u }\ge\text{ 10}[/tex]Step 2: Solve the two inequalities separately
[tex]\begin{gathered} 4u\text{ + 1 }\leq\text{ -3} \\ 4u\text{ }\leq\text{ -3 -1 } \\ 4u\text{ }\leq\text{ -4} \\ u\text{ }\leq\text{ }\frac{-4}{4} \\ u\text{ }\leq\text{ -1} \end{gathered}[/tex][tex]\begin{gathered} -2u\text{ }\ge\text{ 10} \\ \text{When you divide inequalities by -2, the sign will change} \\ \frac{-2u}{-2}\text{ }\leq\text{ }\frac{10}{-2} \\ u\text{ }\leq\text{ -5} \end{gathered}[/tex]
Final answer
[tex](-\infty,\text{ -5\rbrack}[/tex]Or
[tex]\lbrack\text{ x }\leq\text{ -5\rbrack or ( -}\infty,\text{ -5)}[/tex]Solve for y:2x – 3y = 5
y = (2x-5)/3
Explanation:
[tex]\begin{gathered} 2x\text{ - 3y = 5} \\ To\text{ solve for y, we need to make y the subject of formula} \end{gathered}[/tex][tex]\begin{gathered} \text{Let's take every other thing not attached to y to the right side of the equation:} \\ -3y\text{ = 5 - 2x} \\ To\text{ make y stand alone, we will divide through by -3} \\ \frac{-3y}{-3}=\text{ }\frac{5-2x}{-3} \\ y\text{ = }\frac{-(5-2x)}{3}\text{ or }\frac{-5\text{ +2x}}{3}\text{ } \\ y\text{ = }\frac{2x\text{ -5}}{3} \end{gathered}[/tex]One canned juice drink is 20% orange juice, another is 10% orange juice. How many liters of each should be mixed together in order to get 10L that is 11% orangeNice?
Let:
x = Liters of 20% orange juice
y = Liters of 10% orange juice
z = Liters of 11% orange juice
so:
[tex]0.2x+0.1y=10\cdot0.11[/tex]so:
[tex]\begin{gathered} 0.2x+0.1y=1.1 \\ y=10-x \\ so\colon \\ 0.2x+0.1(10-x)=1.1 \\ 0.2x+1-0.1x=1.1 \\ 0.1x=0.1 \\ x=\frac{0.1}{0.1} \\ x=1 \\ so\colon \\ y=10-1=9 \end{gathered}[/tex]Answer:
1 liters of 20% orange juice
9 liters of 10% orange juice
Find the scale factor for 8 in : 2 ft
Explanation
to solve this we need to get the ratio, to do this get the same unit measure in both sides of the quotient
so
[tex]8\text{ in : 2 ft}[/tex]since
[tex]1\text{ ft=12 in}[/tex]replace,
[tex]\begin{gathered} 8\text{ in : 2 ft} \\ 8\text{ in : 2}(12\text{ in)} \\ 8\text{ in: 24 in} \\ \text{divide both sides by 8} \\ \frac{8\text{ in}}{8}=\frac{24\text{ in}}{8} \\ 1\text{ in:3 in} \end{gathered}[/tex]it means the scales factor is
[tex]1\colon3[/tex]Identify the parent function of f(x) = -×^2+2
The given function is
[tex]f(x)=-x^2+2[/tex]The parent function refers to the simplest function possible.
Hence, the parent function is[tex]f(x)=x^2[/tex]More and more people are purchasing food from farmers' markets. As a consequence, a market researcher predicts that the number of farmers' markets will increase by 5% each year. If there are 7,700 farmers' markets this year, how many will there be in 5 years?
Given:
A market researcher predicts that the number of farmers' markets will increase by 5% each year
There are 7,700 farmers' markets this year
we will the number of farmers' markets after 5 years
So, we will use the following formula:
[tex]A=P\cdot(1+r)^t[/tex]We will calculate (A) when P = 7700, r = 5% and t = 5
so,
[tex]A=7700\cdot(1+\frac{5}{100})^5=7700\cdot1.05^5=9827.368[/tex]Rounding to the nearest whole number
so, the answer will be 9827
I need help with this question please! I have options to choose from also. Also the graph below the wording is just option A
The correct option is D
Explanation:Given the function:
[tex]f(x)=x^2-5x+6[/tex]This may be written as:
[tex]y=x^2-5x+6[/tex]For x = -5, -4, -3, -2, -1, 0, 1, 2, 3, 4, 5
we need to find the corresponding values for y.
For x = -5
y = (-5)^2 - 5(-5) + 6
= 56
For x = -4
y = (-4)^2 - 5(-4) + 6
= 42
For x = -3
y = (-3)^2 - 5(-3) + 6
= 30
For x = -2
y = (-3)^2 - 5(-2) + 6
= 20
For x = -1
y = (-1)^2 - 5(-1) + 6
= 12
For x = 0
y = (0)^2 - 5(0) + 6
= 6
For x = 1
y = (1)^2 - 5(1) + 6
= 2
For x = 2
y = (2)^2 - 5(2) + 6
= 0
For x = 3
y = 3^2 - 5(3) + 6
= 0
For x = 4
y = 4^2 - 5(4) + 6
= 2
For x = 5
y = 5^2 - 5(5) + 6
= 6
By inspection, we see that the correct option is D
The school that Imani goes to is selling tickets to a spring musical. On the first day of ticketsales the school sold 6 senior citizen tickets and 8 child tickets for a total of $122. The schooltook in $167 on the second day by selling 9 senior citizen tickets and 8 child tickets. WriteaSOE and solve it to find the price of a senior citizen ticket and the price of a child ticket
Define the system of equations to solve the problem
Take x as the price of a senior citizen ticket and y as the price of a child ticket
[tex]\begin{gathered} 6x+8y=122 \\ 9x+8y=167 \end{gathered}[/tex]Solve the system
[tex]\begin{gathered} 6x+8y=122 \\ 8y=122-6x \\ 9x+8y=167 \\ 8y=167-9x \end{gathered}[/tex][tex]\begin{gathered} 122-6x=167-9x \\ 9x-6x=167-122 \\ 3x=45 \\ x=\frac{45}{3} \\ x=15 \end{gathered}[/tex][tex]\begin{gathered} 8y=122-6x \\ y=\frac{122-6x}{8} \\ y=\frac{122-6\cdot15}{8} \\ y=\frac{122-90}{8} \\ y=\frac{32}{8} \\ y=4 \end{gathered}[/tex]The price of a senior citizen ticket is $15 and for child is $4
Match the appropriate graph to each equation. t(x)= 1/x+3t(x) = -1/x +3
The graph of the function is attached below.
[tex]t(x)=\frac{1}{x+3}[/tex]This matches with the 3rd graph.
Part B
The graph of the function is attached below
[tex]t(x)=-\frac{1}{x}+3[/tex]This matches with the 2nd graph.
Determine if the following equation is linear if the equation is linear converted to standard form AX+by=c
Given the equation:
[tex](-10+y^2)-y^2=-7x+10[/tex]To determine if the equation is a linear equation, the first step is to simplify it. To do so, erase the parentheses and simplify the like terms:
[tex]\begin{gathered} (-10+y^2)-y^2=7x+10 \\ -10+y^2-y^2=7x+10 \\ -10+0y^2=7x+10 \\ -10+0y=7x+10 \end{gathered}[/tex]The terms "+y²" and "-y²" canceled each other, this is why the variable y is multiplied by zero. Then the only variable left is "x", which suggests that the equation represents a vertical line.
To write this equation in standard form, you have to pass the x-term to the left side of the equation and the constant to the right side of it:
[tex]\begin{gathered} -10+0y=-7x+10\text{ \rightarrow add 10 to both sides of the equation} \\ -10+10+0y=-7x+10+10 \\ 0y=-7x+20\text{ \rightarrow add 7x to both sides of the equation} \\ 0y+7x=-7x+7x+20 \\ 0y+7x=20 \\ 7x+0y=20 \end{gathered}[/tex]The line written in standard form is 7x+0y=20.
Vertical lines are considered to be linear equations.
Over 12 hours, the water in Julia's pool drained a total of 534.72 liters. It drained the same number of liters each hour. Write an equation to represent the change in the number of liters of water in Julia's pool each hour.
Answer:
the pool lost 44.56 liters per hour
Step-by-step explanation:
Suppose z varies directly with x and inversely with the square of y. If z = 18 when I = 6 and y = 2, what is z when I 7 and y = 7? Z =
It is given that z varies directly with x and inversely with the square of y so it follows:
[tex]z=k\frac{x}{y^2}[/tex]It is also given that z=18 when x=6 and y=2 so it follows:
[tex]\begin{gathered} 18=k\frac{6}{2^2} \\ k=\frac{18\times4}{6} \\ k=12 \end{gathered}[/tex]So the equation of variation becomes:
[tex]z=12\frac{x}{y^2}[/tex]Therefore the value of z when x=7 and y=7 is given by:
[tex]\begin{gathered} z=\frac{12\times7}{7^2} \\ z=\frac{12}{7} \\ z\approx1.7143 \end{gathered}[/tex]Hence the value of z is 12/7 or 1.7143.
A washer and dryer cost $911 combined the washer cost $61 more than the dryer. What is the cost of the dryer?
ANSWER:
$425
STEP-BY-STEP EXPLANATION:
Let w be the price of the washer and d be the price of the dryer, we can establish the following system of equations:
[tex]\begin{gathered} w+d=911 \\ \\ w=d+61 \end{gathered}[/tex]We substitute the second equation into the first and solve for d, like this:
[tex]\begin{gathered} d+61+d=911 \\ \\ 2d=911-61 \\ \\ d=\frac{850}{2} \\ \\ d=\text{\$}425 \end{gathered}[/tex]Therefore, the price of the dryer is $425.
In 2018 the scores of students on the May SAT had a normal distribution with mean u = 1450 and a standard deviation of o = 120.a. What is the probability that a single student randomly chosen from all those taking the test scores 1500 or higher?b. If a sample of 50 students is taken from the population, what is the probability that the sample mean score of these students is 1470 or higher?
From the question,
[tex]\begin{gathered} \mu\text{ = 1450, } \\ \sigma\text{ = 120} \end{gathered}[/tex]a. We are to find the probability that a single student randomly chosen from all those taking the test scores 1500 or higher?
we will do this using
[tex]\begin{gathered} P(x<\text{ z) such that } \\ z\text{ = }\frac{x\text{ -}\mu}{\sigma} \end{gathered}[/tex]From the question, x = 1500.
Therefore
[tex]\begin{gathered} z\text{ =}\frac{1500\text{ - 1450}}{120} \\ z\text{ = }\frac{50}{120} \\ z\text{ = 0.417} \end{gathered}[/tex]applying z - test
[tex]\begin{gathered} P(xThus, the probability that a single student is randomly chosen from all those taking the test scores 1500 or higher is approximately 34%b. From the question
[tex]\begin{gathered} n\text{ = 50, }^{}\text{ }\mu\text{ = 1450} \\ \bar{x}\text{ = 1470},\text{ }\sigma\text{ = 120} \end{gathered}[/tex]we will be using
[tex]\begin{gathered} z\text{ = }\frac{\bar{x}\text{ - }\mu}{\frac{\sigma}{\sqrt[]{n}}} \\ \end{gathered}[/tex]inserting values
[tex]\begin{gathered} z\text{ = }\frac{1470\text{ - 1450}}{\frac{120}{\sqrt[]{50}}} \\ z\text{ = }20\text{ }\times\frac{\sqrt[]{50}}{120} \\ z\text{ = }\frac{\sqrt[]{50}}{6} \\ z\text{ = 1.18} \end{gathered}[/tex]Applying z-test
[tex]\begin{gathered} P(xHence,
The probability that the sample mean score of these students is 1470 or higher is approximately 12%
15h - 13h - h + 3= 7
Answer:
[tex]h=4[/tex]Explanation: We need to solve for h in the given equation, which is:
[tex]15h-13h-h+3=7[/tex]Isolating unknowns and constants:
[tex]\begin{gathered} 15h-13h-h+3=7\rightarrow15h-14h+3=7 \\ \therefore\rightarrow \\ 15h-14h=7-3=4 \\ \therefore\rightarrow \\ 15h-14h=4 \end{gathered}[/tex]Simplifying gives:
[tex]\begin{gathered} 15h-14h=4 \\ \therefore\rightarrow \\ h=4 \end{gathered}[/tex]Evaluate: 6+ [8x(5-1)]
6+ [8x(5-1)]
First, solve the parenthesis:
6+ [8x4]
Then the brackets:
6+ 32
Finally, add both numbers.
38
Need help. The ps5 cost 610 dollars And Be gets 100 dollars every week
Let x be the number of weeks after Mohammed started to save up. Since he receives $100 every week, then, after x weeks, he would receive 100x dollars.
Since he already had $50 at the beginning, then, the total amount of money y that he has saved after x weeks, is:
[tex]y=100x+50[/tex]Since the cost of the PS5 is $610, then, set y=610 and solve for x to find the number of weeks that he will need to save money:
[tex]\begin{gathered} y=610 \\ \Rightarrow610=100x+50 \\ \Rightarrow610-50=100x \\ \Rightarrow560=100x \\ \Rightarrow\frac{560}{100}=x \\ \Rightarrow x=5.6 \end{gathered}[/tex]He will need to save for at least 5.6 weeks. Nevertheless, he only receives money once a week and 5 weeks won't be enough for buying the PS5. Then, he needs to save for 6 weeks.
A cylindrical can has a radius of 6 inches and a height of 15 inches. Find the volumeof the can.
let's remember the formula to find the volume of a cylinder
Let's apply the formula with the values that we have in the problem.
The volume of the cylindrical can is 540π inches^3 or 1696.46 inches^3.
Why do dividing functions have 4 end behaviors
Since the dividing function has discontinuity in x and y, we can see that it would have 4 end behaviours
Which statement describes a key feature of the function g if g(x) =f(x)-7
The graph of the function f(x)=e^x is given.
To determine the function g(x),
g(x)=f(x)-7.
Then the graph of function g(x) is
Then from the graph above , the horizontal asymptote is y=-7.
Hence the correct option is D.
What is the area of this figure?5 in5 in12 in23 in18 in17 in
The area of the figure is 331 square inches
Explanation:The area of the shape can be obtained by:
Treating the shape as a rectangle with side lengths 23 in and 17 in
Finding the area of the rectangle
Finding the area of the small portion cut, which is a rectangle with side lengths 5 in and 12 in.
Subtracting the area of the small portion from the area of the big rectangle.
Area of the big rectangle = 23 * 17 = 391 in^2
Area of the small portion = 5 * 12 = 60 in^2
Area of the shape = 391 - 60 = 331 in^2
Nine hundred people who attended a movie were asked whether they enjoyed it. The table shows the results.Did Not EnjoyTotalChildrenAdultsTotalEnjoyed461277738114162900How many more children were surveyed than adults? Enter a numerical answer only
Given:
Total number of people that attended = 900
The total number of adults that attended = 277 + 114 = 391
Total number of children that attended = Total number of people - number of adults
= 900 - 391 = 509
To find how many more children were surveyed than adults, subtract the number of adults from the number of children.
Thus, we have:
Number of children surveyed than adults = 509 - 391 = 118
Therefore, 118 more children were surveyed more than adults.
Let's complete the table below:
ENJOYED DID NOT ENJOY TOTAL
CHILDREN 461
What is the difference between 3xg and gº? .
EXPLANATION
The difference is that 3*g is a multiplication that give us a Real number and g° is a degree number.