Step-by-step explanation:
The ratio of the length to the width that is- length:width = 5:3
Take x as a common value,
5x= length
3x= width
Width of the rectangle= 1500 cm
3x= 1500 cm
x= 1500/3
x= 500 cm
Length of the rectangle= 5x
x=500 cm
Length= 5*500
=2500 cm
Length of the rectangle= 2500 cm
Shawn pays a rate of 35.55 mills in property tax on a home with an assessed value of $63,500. What is his property tax?
Answer:
$2257.425
Explanation:
A rate of 35.55 mills means that they have to pay 35.55 per each $1000 in the assessed value. If the assessed value is 63,500, we can calculate his property tax as
[tex]63,500\times\frac{35.55}{1000}=2257.425[/tex]Therefore, the answer is $2257.425
A new born child receives a $8,000 gift toward a college education from her grandparents. How much will the $8,000 be worth in 17 years if it is invested at 72% compounded quarterly?It will be worth $(Round to the nearest cent)
The money will be worth $618111016.19 at the end of 17 years
Explanation:Initial amount received, P = $3000
Interest rate, r = 72%
r = 72/100
r = 0.72
Number of times compounded in a year, n = 4
Time, t = 17 years
Amount after 17 years will be calculated as:
[tex]A=P(1+\frac{r}{n})^{nt}[/tex]Substitute P = 8000, r = 0.72, n = 4, and t = 17 into the formula above
[tex]A=8000(1+\frac{0.72}{4})^{4(17)}[/tex][tex]\begin{gathered} A=8000(1+0.18)^{68} \\ A=8000(1.18)^{68} \end{gathered}[/tex]A = $618111016.19
The money will be worth $618111016.19 at the end of 17 years
In Mr. Peter's class, 75% of the students have a pet. There are 15 students with pets in the class. How many total students are in the class?
Answer:
20 Students
Explanation:
Let the total number of students in the class = x
Number of students that have pets = 15
Percentage of students that have pets = 75%
Therefore:
[tex]75\%\text{ of x=15}[/tex]We then solve for x.
[tex]\begin{gathered} \frac{75}{100}\times x=15 \\ 0.75x=15 \\ x=\frac{15}{0.75} \\ x=20 \end{gathered}[/tex]We have 20 students in total in the class.
Find the distance between the points (4,1) and (2,4) using distance formula
Given:-
[tex](4,1)(2,4)[/tex]To find the distance.
So the distance formula is,
[tex]d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]Substituting we get,
[tex]\begin{gathered} d=\sqrt{(2-4)^2+(4-1)^2} \\ d=\sqrt{-2^2+3^2} \\ d=\sqrt{4+9} \\ d=\sqrt{13} \end{gathered}[/tex]So the required distance is root 13.
The first part of the function rule for the values in the table below is Y equals X over two. What is the complete function rule?
Given:
The tabular representation having different values of x and y.
Required:
The relation between x and y.
Explanation:
When x = 6 and y = 2,
[tex]y\text{ = }\frac{6}{2}\text{ = 3 }\Rightarrow\text{ 3 - 1 = 2 = x}[/tex]When x = 8 and y = 3,
[tex]y\text{ = }\frac{8}{2}\text{ = 4 }\Rightarrow\text{ 4-1 = 3}[/tex]When x = 10 and y = 4,
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4. If line segment AB has coordinates A(-2,4) and B(2,0) and line segment
CD has coordinates C(3,4)and D(-3,-2), how would you describe these two
line segments?
A: neither
B: perpendicular
C: parallel
Answer:
B
Step-by-step explanation:
[tex]m_{\overline{AB}}=\frac{4-0}{-2-2}=-1 \\ \\ m_{\overline{CD}}=\frac{-2-4}{-3-3}=1 [/tex]
Since the slopes are negative reciprocals of each other, and since they intersect, they are parallel.
Find m∠1 I need help please
Answer: 70
Step-by-step explanation: 180-110=70
because of isosceles, so ∠1=70
Can you explain this math to me please I’ve never seen it before and don’t understand
For a quadratic function in standard form,
[tex]\begin{gathered} \text{a = coefficient of x}^2 \\ b\text{ = coeffcient of x} \\ c=\text{ the constant term} \end{gathered}[/tex]For the polynomial f(x),
a = 2, b = -3 and c = 4
For the polynomial g(x)
a = 4, b = -6, c = 10
For the polunomial h(x),
a = 7, b = 0, c = 8
For the polynomia p(x),
a = 1, b = -10, c = 0
Matt and Amy each had summer jobs. Matt worked at a restaurant as a bus boy. He earned $10 per hour, plus tips. Amy worked as a dog-groomer. She earned $8 per hour, plus tips.A) Create an equation to represent their total earnings in each situation. Explain what each of the variables represent.
Given:-
Matt and Amy each had summer jobs. Matt worked at a restaurant as a bus boy. He earned $10 per hour, plus tips. Amy worked as a dog-groomer. She earned $8 per hour, plus tips.
To find:-
An equation to represent their total earnings in each situation.
The average of 13, 15, 20 and x is 18. What is the value of x?
x will be equal to 24.
Given,
There are 4 numbers:
13, 15, 20, and x.
Average of all numbers = 18.
We know that,
Average = ( sum of all numbers) / ( total numbers)
In this case,
Average = ( 13 + 15 + 20 + x) / 4
According to the question,
18 = (48 + x) / 4
=> 72 = 48 + x
=> x = 72 - 48
=> x = 24.
So, in order to make the average equal to 18, x should be equal to 24.
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14. A waterway contains 10.3 milligrams of an impurity per gallon of water. How many micrograms of impurity arepresent per liter of water?
1) Gathering the data
10.3 mg of impurity per gallon of water
? μg of impurity per liter?
2) Since this is a matter of units conversion, then let's work remembering
the Metrical and Customary equivalences:
1 μg = 0.001 mg
1 gallon = 3.78 liters
3) As we have a ratio, let's write it as a ratio:
[tex]undefined[/tex]Real number between 0 and 6 will be picked according to the probability distribution shown in the figure. Regions under the curve are liable with A, B, C, and D. The area of each is shown in the table. Use the figure and table to answer the parts
Part A
The probability that a real number between 1 and 4 is picked
P=PB+PC
P=0.15+0.50
P=0.65Part B
The probability that a real number between 2 and 6 is picked
P=PC+PD
P=0.50+0.30
P=0.80Find the circumference of a circle with a diameter of centimeters. Round your answer to the nearest centimeter.
Circumference = 2* pi * r
r = radius
r = diameter/2
r = 50/2
r = 25 cm
Circumference = 2*3.14 * 25
Circumference = 157 cm
Result = 157 cm
The second choice
Determine the required value of a missing probability to make the distribution a discrete probability distribution… p(4) =
The table given showed the discrete probability distribution for random variables 3 to 6 and their corresponding probability except for the probability of 4
It should be noted that for a probability distribution, the cummulative probabibility (that is the sum of all the probability) must be equal to one.
This means that
[tex]P(3)+P(4)+P(5)+P(6)=1[/tex]From the given table, it can be seen that
[tex]\begin{gathered} P(3)=0.32 \\ P(4)=\text{?} \\ P(5)=0.17 \\ P(6)=0.26 \end{gathered}[/tex]Then, p(4) is calculated below
[tex]\begin{gathered} P(3)+P(4)+P(5)+P(6)=1 \\ 0.32+P(4)+0.17+0.26=1 \\ P(4)+0.32+0.17+0.26=1_{} \\ P(4)+0.75=1 \\ P(4)=1-0.75 \\ P(4)=0.25 \end{gathered}[/tex]Hence, P(4) is 0.25
The midpoint of AB is M(7,-2). If the coordinates of A are (8,3), what are thecoordinates of B ?
The coordinates are ordered pairs with the x value listed first.
The change in x position is, 8-7=1
The change in y position is, 3-(-2)=5
Since the midpoint is halfway between A and B, the change will stay the same,
So, for B,
x is 7-1=6
y is -2-5=-7
The coordinnates of B is (6,-7)
The graphs of the functions g and h are shown below. For each graph, find the absolute maximum and absolute minimum. If no such value exists, click on "None".
Assume that the dashed line shown is a vertical asymptote that the graph does not cross.
For the graph g, the absolute maximum is 2 and the absolute minimum is -4.
Similarly, for graph h, the absolute maximum is 3 and the absolute minimum is -5.
Absolute Maximum of a Graph:
The absolute maximum of a graph is the point on the graph with the highest y-value. There can only be one absolute maximum of a graph.
Absolute Minimum of a Graph:
The absolute minimum of a graph is the point on the graph with the lowest y-value. There can only be one absolute minimum of a graph.
Given,
Here we have the two graph called g and h.
Now, we need to find the absolute maximum and minimum from it.
AS per the given definition, we know that,
For graph g,
The absolute maximum is 2 and the absolute minimum is -4.
Similarly, for graph h, the absolute maximum is 3 and the absolute minimum is -5.
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Explain why the product of 20 x 30 is equal to 600.
BIU
Answer:
600
Step-by-step explanation:
2 X 3 = 6
20 has one 0
30 has one 0
one 0 and one 0 is two 0s
6 plus two 0s = 600
Use the distance formula, slopes and your knowledge of characteristics of different
types of quadrilaterals to determine the type of quadrilateral formed by the
following four points (-3, 1) , (-2, 3) , (0, 4) , (-1, 2)
This quadrilateral is square . It have same length of side.
How to Find type of quadrilaterals?In geometry, a quadrilateral is a four-sided polygon with four edges and four corners. The angles stood present at the four vertices or corners of the quadrilateral. If ABCD is a quadrilateral, the angles of the vertices are A, B, C, and D. The sides of a quadrilateral are AB, BC, CD, and DA. The four vertices of the quadrilateral ABCD are A, B, C, and D.The diagonals are formed by connecting the quadrilateral's opposite vertices.Quadrilaterals are typically four-sided shapes such as rectangles, squares, and trapezoids.In a concave quadrilateral, one interior angle is greater than 180°, and one of the two diagonals lies outside the quadrilateral.A convex quadrilateral's interior angles are all less than 180°.Therefore,
From question the coordinates of A,B,C,D are given as ,
A = (-3, 1) B = (-2, 3) C = (0, 4) D = (-1, 2)
We use distance formula :
Distance = √(x2 -x1)²+(y2 - y1)²
AB = √(-2 + 3)²+(3 - 1)² = √(5)
BC = √(0+2)²+(4–3)² = √5
CD = √(-1 –0)²+(2–4)² =√5
DA = √(-1 +3)²+(2–1)² =√5
We get the distance is √5 for all points, so the type of quadrilateral is square.
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statistics classifying samples (I am not sure if this is B or C)
ANSWER :
C.
EXPLANATION :
Cluster sampling divides the population into smaller groups known as clusters.
Then randomly selecting among these clusters to form a sample.
In A, there's no grouping.
In B, there is a grouping and he randomly chooses 9 groups and selects all of the passengers.
In C, there is a grouping and he selects 12 passengers at random from each group
The best scenario that represents a cluster sampling is C.
Mrs barker wants to tile her washroom floor. The area of the washroom floor is 6.75 square metres. She determines that she will use 300 square tiles. What are the dimensions of the tiles, in centimetres?
ANSWER
15 centimeters
EXPLANATION
First, we have to find the area of the washroom floor in square centimeters, by multiplying the area in square meters by 10,000 or, in other words, moving the decimal point 4 units to the right,
[tex]6.75m^2=6.75\times10,000cm^2=67,500cm^2[/tex]Now, we know that Mrs. Barker will use 300 square tiles, so the area of each tile must be,
[tex]A_{tile}=\frac{A_{floor}}{number\text{ }of\text{ }tiles}=\frac{67,500cm^2}{300}=225cm^2[/tex]Thus, if the tiles are squared, the side length of each tile is the square root of the area of each tile,
[tex]s=\sqrt{A_{tile}}=\sqrt{225cm^2}=15cm[/tex]Hence, the side length of each tile is 15 cm.
Please give me the answers asap the time is running down
Explanation
Given the question
[tex]|x|<13[/tex]To get the values of x, we will consider two possibilities which are:
[tex]\begin{gathered} x\text{ being positive},\text{ so that} \\ x<13 \end{gathered}[/tex]And
[tex]\begin{gathered} x\text{ being negative} \\ -x<13 \\ x>-13 \end{gathered}[/tex]Therefore, the value of x is
[tex]\begin{bmatrix}\mathrm{Solution\colon}\: & \: -13So the correct option is
[tex]\begin{bmatrix}\mathrm{Solution\colon}\mleft\lbrace x|\: \mright? & \: -13Option A is correctThe first option is correct
What is the value of x? Enter your answer in the box. x =
The value of x from the given isosceles triangle is 8 units.
The measures of sides of triangle are given AB=4x-10, AC=5x-22 and BC=3x+2.
What is an isosceles triangle?Isosceles triangles are those triangles that have at least two sides of equal measure and two base angles are equal.
Here, AC = BC
⇒ 5x-22 = 3x+2
⇒ 5x-3x = 22+2
⇒ 3x = 24
⇒ x = 8 units
Therefore, the value of x from the given isosceles triangle is 8 units.
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What is the digit in the units place of the sum of 1^1+ 2^2+ 3^3+ 4^4 +.....+ 99^99 + 100^100?
Let us write down first few factors
1^1 = 1
2^2 = 4
3^3 = 27
4^4 = 256
5^5 = 3125
6^6 = 46656
.
.
.
100^100 = ... finish in zero
The last two digits in the sum would be 20
The digit in the unit would be 0
In how many ways can the letters in the word PAYMENT be arranged using 4 letters?A. 42B. 840C. 2520D. 1260
The word PAYMENT has 7 letters. They can be arranged in groups of 4 like shown below:
PYNT, TA
You start a trip when your odometer reads 23,672 miles, and you have a full tank of gas. After
driving a few hours, you fill up your tank. If you buy 16.5 gallons and your odometer reads
23,927, how many miles to the gallon are you getting, rounded to the nearest tenth of a gallon.
I need helppp with example pliss
Answer:
15.6 MPG
Step-by-step explanation:
You start a trip when your odometer reads 23,672 miles, and you have a full tank of gas. After driving a few hours, you fill up your tank. If you buy 16.5 gallons and your odometer reads 23,927, how many miles to the gallon are you getting, rounded to the nearest tenth of a gallon.
You went 23,927 - 23,672 = 255 miles
Because you started on a full tank, you went 255 miles on 16.5 gallons
to figure MPG:
255/16.5 = 15.4545... MPG
rounded to nearest 10th of gallon:
15.6 MPG
Solve the quadratic equation x2 − 6x + 13 = 0 using the quadratic formula. What is the solution when expressed in the form a ± bi, where a and b are real numbers?
The given quadratic equation is:
[tex]x^2-6x+13=0[/tex]The quadratic formula is given by the equation:
[tex]x=\frac{-b\pm\sqrt[]{b^2-4ac^{}}}{2a}[/tex]From the given quadratic equation;
[tex]a=1;b=-6\text{ and c=13}[/tex]Thus, we have:
[tex]x=\frac{-(-6)\pm\sqrt[]{(-6)^2-4(1)(13)}}{2(1)}[/tex][tex]\begin{gathered} x=\frac{6\pm\sqrt[]{36-52}}{2} \\ x=\frac{6\pm\sqrt[]{-16}}{2} \\ In\text{ complex form, the }\sqrt[]{-16}=4i \\ \text{Thus, we have:} \\ x=\frac{6\pm4i}{2} \\ x=\frac{6}{2}\pm\frac{4i}{2} \\ x=3\pm2i \end{gathered}[/tex]Hence, the correct option is Option A
Daylyn wants to win headphones . In addition to his grandmother and uncle, some friends of his agree that each one will give him a $5 donation . Some other friends agree that each one will pay him $0.25 for every correct answer. The number of friends who donate $ 5 to Daylyn is 3 times the number who pays him for correct answers. Write and solve an equation to find the number of friends who must pay him $0.25 for each correct answer in order for Daylyn to meet his goal
Let
x ------> number of friends of his agree that each one will give him a $5 donation
y -----> the number of friends who must pay him $0.25 for each correct answer
so
to win headphones-------> $350
we have that
x=3y -------> equation A
5x+0.25y=350 -------> equation B
substitute equation A in equation B
5(3y)+0.25y=350
solve for y
15y+o.25y=350
15.25y=350
y=22.95
therefore
the answer is 23 friends who must pay him $0.25 for each correct answerWhich of the following graphs represent the system of equations f(x) = x2 + 2x + 2 and g(x) = –x2 + 2x + 4?
The Solution:
Given:
[tex]\begin{gathered} f(x)=x^2+2x+2 \\ \\ g(x)=-x^2+2x+4 \end{gathered}[/tex]We are required to determine the graphs of the given functions.
Below is the graph of the function:
Thus, the correct answer is:
top question says: Triangle ABC can be taken to triangle A'B'C' using rigid motions and a dilation. help me pls
If triangle ABC can be taken to triangle A'B'C', it means that they are similar triangles. If tow triangles are similar, it means that the ratio of their corresponding sides are equal. Thus, we have
A'B'/AB = B'C'/BC = A'C'/AC
Thus, looking at the options, the true equations are
A) A'C'/B'A' = AC/BA
D) CA/C'A' = CB/C'B'
E) A'B'/AB = C'B'/CB
If we look at these options the ratios are always the same
it says i need to find the shortest distance between the point and the line for geometry honors, how would i figure it out
The given line equation is,
[tex]3x-y=-6[/tex]The given point is ,
[tex](5,1)[/tex]The graph will look like this,
let us rewrite the line equtaion as ,
[tex]3x-y+6=0[/tex]now, let us compare with the general equation of line,
[tex]Ax+By+C=0[/tex]then, A= 3,B=-1 and c= 6.
let us use the formula,
[tex]\begin{gathered} d=\frac{|Ax+By+c|}{\sqrt[]{A^2+B^2}} \\ d=\frac{|3\times5+(-1)\times1+6|}{\sqrt[\square]{3^2+(-1)^2}} \\ d=\frac{|15-1+6|}{\sqrt[\square]{9+1}} \\ d=\frac{20}{\sqrt[\square]{10}} \\ d=6.32 \end{gathered}[/tex]The shortest distance is 6.32 .