The formula to find the sum of the interior angles of a polygon is given below,
[tex]\text{Sum of angles of polygon = (n-2)180}^0[/tex]Number, n, of sides of a regular pentagon is 5 i.e n = 5,
To find the sum of angles in a regular pentagon, substitute for n into the formula above,
[tex]\text{Sum of angles of a pentagon=(5-2)180}^0=3\times180^0=540^0[/tex]To find the measure of each angle of the pentagon, the formula is given below
[tex]\begin{gathered} for\text{ each interior angle=}\frac{Sum\text{ of angles}}{n} \\ \text{Where n = 5} \\ \text{For each interior angle=}\frac{540^0}{5}=108^0 \end{gathered}[/tex]Hence, each interior angle is 108°
Solve the following equation for X 5x+7y=19 X= ?
1) We can solve this equation for x, by doing the following algebraic manipulation:
[tex]\begin{gathered} 5x+7y=19 \\ \\ 5x+7y-7y=19-7y \\ \\ 5x=19-7y \\ \\ \frac{5x}{5}=\frac{19}{5}-\frac{7y}{5} \\ \\ x=-\frac{7}{5}y+\frac{19}{5} \\ \\ x=\frac{19-7y}{5} \end{gathered}[/tex]2) In this problem, we can't go any further than that. So, that is the answer.
At a fundraiser , a sorority is able to raise $5 less than four times the amount of money a fraternity raises
All together they raised $115
First question what is known is the situation?
Second question what is unknown in the situation
Third question how do I write an equation that represents the situation use at to represent the fraternity
NEED HELP ASAP I WILL MARK YOU BRAINLIEST NO LINKS PLEASE AND THANK YOU
An equation that represents the situation used to represent the amount that the fraternity raises is; x + (4x - 5) = 115
How to solve Algebra Word Problems?Let the amount of money raised by the fraternity be x.
Now, we are told that the sorority raises $5 less than four times the amount that a fraternity raises. Thus;
Amount raised by Sorority = $(4x - 5)
Together, we are told that they raised $115. Thus, the equation will be;
x + (4x - 5) = 115
5x - 5 = 115
5x = 115 + 5
5x = 120
x = 120/5
x = $24
Read more about Algebra Word Problems at; https://brainly.com/question/28339921
#SPJ1
The value V of an item after t years is given by the following formula, assuming linear depreciation,V = C - Crt.where C is the original cost and r is the rate of depreciation expressed as a decimal.If you buy a car for $7191 and it depreciates linearly at a rate of 5% per year, what will be its value after 9 months? Round youranswer to the nearest cent.
Here C=$7191
r=0.05
t=9 months=0.75 years
The value of the car will be
[tex]V=7191-7191\times0.05\times0.75\Rightarrow V=7191-269.6625\Rightarrow V=6921.34[/tex]Hence the value of the car will be $6921.34.
the square practice x² + 6x + 9 = 0
x = -3 twice
Explanation:x² + 6x + 9 = 0
Since the method for solving the question isn't specified, we will be using factorisation method to solve for x.
factors of 9 = 1, 3, 9
The two numbers when multiplied gives 9 and when added gives 6 are +3 and + 3.
using factorisation method:
x² + 3x + 3x + 9 = 0
x(x + 3) + 3(x + 3) = 0
(x + 3)(x + 3) = 0
(x+3) = 0 or (x+3) = 0
x = -3 or x = -3
x = -3 twice
The second method is because of the square practice in the question.
Using complete the square:
x² + 6x + 9 = 0
x² + 6x = -9
we half the coefficient of x and the square the result
coefficient of x = 6
1/2 of coefficient of x = 6/2
square of the result = (6/2)² = 3² = 9
Add the above result from both sides of the equation:
x² + 6x + 9 = -9 + 9
(x + 3)² = 0
square root both sides:
x + 3 = +/- √0
subtract 3 from both sides:
x +3 -3 = -3 +/-√0
x = -3 + 0 or -3 - 0
x = -3 twice
Answers : • center c and scale factor 2• center a and scale factor 5• center c and scale factor 1• center a and scale factor 2
In order to find the scale factor of the dilation of ΔABC, we just need to divide any pair of the corresponding sides of both triangles. We have that the division of the corresponding sides will be always the same:
[tex]\frac{A^{\prime}C^{\prime}}{AC}=\frac{B^{\prime}C^{\prime}}{BC}=\frac{A^{\prime}B^{\prime}}{AB}=\text{scale factor}[/tex]We are going to choose the first division:
[tex]\frac{A^{\prime}C^{\prime}}{AC}=\text{scale factor}[/tex]Finding the scale factorWe have that AC = 5 and A'C' = 10:
Then:
[tex]\begin{gathered} \frac{A^{\prime}C^{\prime}}{AC}=\text{scale factor} \\ \downarrow \\ \frac{10}{5}=2 \end{gathered}[/tex]The scale factor is 2.
And since the point C and C' are the same, the center is C.
Answer- A. center C and scale factor 2
if you could please try to answer quickly my brainly keeps crashing
The lateral area of a cylinder is given by:
[tex]L=2\pi rh[/tex]where r represents the radius and h represents the height.
Then,
h=13m
In this case, we have the diameter. However, the radius is the half value of the diameter.
Then,
r=d/2=6m/2=3m
Replacing:
[tex]\begin{gathered} L=2\pi(3m)(13) \\ L=245m^2 \end{gathered}[/tex]Hence, the lateral area is 245m².
I'll send the question 2-x>8
The given inequality is
[tex]2-x>8[/tex]We subtract 2 from each side.
[tex]\begin{gathered} 2-2-x>8-2 \\ -x>6 \end{gathered}[/tex]Then, we multiply the inequality by -1.
[tex]\begin{gathered} -x\cdot-1<6\cdot-1 \\ x<-6 \end{gathered}[/tex]Hence, the answer is b.Claim: The mean pulse rate (in beats per minute) of adult males is equal to 68.9 bpm. For a random sample of 134 adult males, the mean pulse rate is 70.1 bpm and the standard deviation is 10.9 bpm. Complete parts (a) and (b) below.
Part A. Express the original claim in symbolic form.
Claim: The mean pulse rate (in beats per minute) of adult males is equal to 68.9 bpm.
Therefore, the original claim in symbolic form is:
ANSWER:
[tex]\mu=68.9\text{ bpm}[/tex]Part B. Identify the null and alternative hypotheses.
[tex]\begin{gathered} H_0\colon\text{ }\mu=68.9\text{ bpm} \\ H_1\colon\mu\ne68.9\text{ bpm} \end{gathered}[/tex][tex]\begin{gathered} H_0\text{ or the null hypothesis will be based to our claim. We will test if the mean pulse} \\ \text{rate of an adult male is equal to 68.9 bpm.} \\ H_1\text{ or the alternative hypothesis is the one that contradicts the null hypothesis. That is } \\ \text{why our H}_a\text{ has the sign of not equal to (}\ne). \end{gathered}[/tex]
can you help me on the Rolling a 7 part
Rolling a 7
Total outcomes=6*6=36
favorable outcomes
1-6
2-5
3-4
4-3
5-2
6-1
tota favorable outcomes=6
so
The probability of rolling a 7 is equal to
P=6/36
simplify
P=1/611. The trigonometric ratio of cos B isPYTHAGOREAN TRIPLE PROBLEMB13590°A125/1212/135/1313/5
From the given right-angled triangle, we have the following:
Hypothenuse side = 13
Opposite side = 12
Adjacent side = 5
Solution
The trigonometric ratio of cos B can be found using the relationship:
[tex]\cos \text{ B = }\frac{Adjacent}{Hypothenus}[/tex]By substituting, we have:
[tex]cos\text{ B = }\frac{5}{13}[/tex]Hence, the answer is 5/13 (option C)
how to solve the volume of sphere and the area of a cylinder.
Consider a sphere of radius r, then the volume of the sphere is given by,
[tex]V=\frac{4}{3}\pi\times r^3[/tex]Here
[tex]\pi=3.14[/tex]Now let us consider a cylinder of with base radius r and height h, as in the figure,
The area is the total area of the base surface and the niddle surface.
This can be written as,
[tex]A=2\pi(h+r)[/tex]Consider a sphere of radius 2 cm, the volume can be calculated as,
[tex]v=\frac{4}{3}\times3.14\times2^3=\frac{4}{3}\times3.14\times2\times2\times2=33.49cm^3[/tex]What is the best estimate for this sum 1/8+1/6=The sum will be close to?
The expression given is
[tex]\frac{1}{8}+\frac{1}{6}[/tex]The sum of the expression will be,
[tex]\frac{1}{8}+\frac{1}{6}=\frac{6+8}{48}=\frac{14}{48}=\frac{7}{24}[/tex]The sum will be
[tex]\frac{7}{24}[/tex]If a line falls on the points (25, 24) and (15, 17), what is its slope? Enter your answer as a fraction in lowest terms. Use a slash mark (7) as the fraction bar.
If a line falls on the points (25, 24) and (15, 17), what is its slope? Enter your answer as a fraction in lowest terms. Use a slash mark (7) as the fraction bar
the slope is
m=(17-24)/(15-25)
m=-7/-10
m=7/10
answer is slope is 7/10Write an equation in slope intercept form for the line that has a slope of 4/5 and passes through (0,7) Mark only one ovalY=7xY=7x-4/5Y=4/5x+7Y=-4/5x+7
Given:
The slope of the line is
[tex]m=\frac{4}{5}[/tex]Passes through the point
[tex](x,y)=(0,7)[/tex]Required:
To find equation in slope intercept form.
Explanation:
The general equation of slope intercept form is
[tex]y=mx+b[/tex]Where, m = slope
b = y-intercept.
Now,
[tex]y=\frac{4}{5}x+b[/tex]Here The line passes through the point (0,7), therefore the y-intercept is 7.
So,
[tex]y=\frac{4}{5}x+7[/tex]Final Answer:
[tex]y=\frac{4}{5}x+7[/tex]A box contains letters, shown as MARCHING. What is the probability of the outcome in that order if letters are drawn one by one (a) with replacement? (b) without replacement?
There are 8 letters in the word MARCHING.
So, the number of letters in the box, N=8
b)
The probabilty of drawing the first letter M is,
[tex]P(M)=\frac{1}{N}=\frac{1}{8}[/tex]If the letter is not replaced, the number of remaining letters in the box is 7.
So, the probabilty of drawing the second letter A is,
[tex]P(A)=\frac{1}{7}[/tex]Similarly, the probabilities of drawing letters R,C,H,I, N and G respectively is,
[tex]\begin{gathered} P(R)=\frac{1}{6} \\ P(C)=\frac{1}{5} \\ P(H)=\frac{1}{4} \\ P(I)=\frac{1}{3} \\ P(N)=\frac{1}{2} \\ P(G)=1 \end{gathered}[/tex]So, the probability of of the outcome in that order if letters are drawn one by one without replacement is,
[tex]undefined[/tex]Jimmy wants to make a pentagonal push pop that is 3.25 inches long with a side length of 0.75 inches. Find the surface area of the push pop.
We are asked to determine the surface area of the figure. To do taht we will add the areas of each of the surfaces of the figure. Since it is a pentagon, we will determine the lateral area of one of the surfaces and multiply the result by 5:
[tex]A_l=5sl[/tex]Where "s" is the side length and "l" is the longitude. Replacing the values:
[tex]A_l=5(0.75in)(3.25in)[/tex]Solving the operations:
[tex]A_l=12.19in^2[/tex]Can help me:coin is flipped 6 times. What is the probability that heads and tails occur an equal number times?
The probability that heads and tails occur an equal number times is 5/16.
From the question, we have
The number of permutations =HHHTTT
The total number of permutations = 6!=720.
Since, there are two groups comprising 3 identical objects, the number of permutations = 720/3!3!=20.
total number of possibilities in the event space= 2^6=64
the required probability = 20/64=5/16.
Probability:
Probability refers to potential. A random event's occurrence is the subject of this area of mathematics. The range of the value is 0 to 1. Mathematics has incorporated probability to forecast the likelihood of various events. The degree to which something is likely to happen is basically what probability means. You will understand the potential outcomes for a random experiment using this fundamental theory of probability, which is also applied to the probability distribution.
To learn more about probability visit: https://brainly.com/question/11234923
#SPJ9
I’m trying to figure out how to do this one ! It’s kind of got me stuck
ANSWER :
The answer is Option 3.
EXPLANATION :
From the problem, we have the equation of the line :
[tex]y=x+3[/tex]First thing to do is check the correctness of the table.
The given values in the table must satisfy the equation.
For Option 1.
Let's check the point (2, 3)
[tex]\begin{gathered} y=x+3 \\ 3=2+3 \\ 3=5 \\ \text{ False!} \end{gathered}[/tex]For Option 2.
Let's check the point (-2, 1)
[tex]\begin{gathered} y=x+3 \\ 1=-2+3 \\ 1=1 \\ \text{ True!} \end{gathered}[/tex]But the point (-2, 1) is not in the graph, so this is false!
For Option 3.
The points are the same with Option 2, so we need to check the graph.
(-2, 1) is on the graph.
(-1, 2) is on the graph.
(0, 3) is on the graph.
(1, 4) is on the graph.
(2, 5) is on the graph.
So this must be the correct table and graph.
enter an equation that describes the propitiatial relationship between the number of days and the number of weeks in a giving length of time
We need to find an equation that describes the relationship between days and week.
We know that one week has 7 days:
So, to find the number of days for a given number of weeks, what we need to do is multiply the number of weeks by 7.
If we call the number of weeks "w" and the number of days "d", the equation that describes the proportional relationship is:
[tex]d=7w[/tex]The number of days is equal to the number of weeks multiplied by 7.
Now with this, we can complete the table of values. For 4 weeks, the number of days is:
[tex]\begin{gathered} d=7(4) \\ d=28 \end{gathered}[/tex]For 5 weeks, the number of days is:
[tex]\begin{gathered} d=7(5) \\ d=35 \end{gathered}[/tex]To complete the next row, we don't need the days, we need the number of weeks. For that, we take our equation and substitute the number of days:
[tex]\begin{gathered} d=7w \\ 42=7w \end{gathered}[/tex]And we solve for "w" by dividing both sides by 7:
[tex]\begin{gathered} \frac{42}{7}=w \\ 6=w \end{gathered}[/tex]Finally, for the last row, we find the number of days in 13 weeks using our equation:
[tex]\begin{gathered} d=7(13) \\ d=91 \end{gathered}[/tex]Find the least-squares regression line y = bo + b₁x through the points
(-2,0), (0,7), (4, 15), (8, 18), (9,24),
and then use it to find point estimates y corresponding to x = 1 and x = 8.
For this problem and to give you practice for the test, use the shortcut method to find bo given that b₁ = 1.9051724137931.
For x = 1, y =
For x = 8, y^=
The values for x = 1, then y = 38.23 and for x = 8, then y^ = 55.375.
Given that, [tex]y = b_{0}+ b_{1}x[/tex]
x y xy xx yy
-2 0 0 4 0
0 7 0 0 49
4 15 60 16 225
8 18 144 64 324
9 24 216 81 576
19 64 420 165 1174 - Total(T)
n = 5
Given line is [tex]y = b_{0}+ b_{1}x[/tex]
Solve for the value of [tex]b_{0}[/tex]
[tex]b_{0} = \frac{Ty*Txx-Tx*Txy}{nTx^{2} -(Tx)^{2} }[/tex]
[tex]= \frac{64*165-19*420}{5*165-(19)^{2} }\\ \\= \frac{10560-7980}{825-361}\\ \\= \frac{2580}{64} = 40.135[/tex]
Solve for the value of [tex]b_{1}[/tex]
[tex]b_{1} = \frac{nTxy-Tx*Ty}{nTx^{2} -(Tx)^{2} }\\ \\= \frac{5*420-19*64}{5*165 - (19)^{2} }\\ \\= \frac{2100-1216}{464}\\ \\= \frac{884}{464} = 1.905[/tex]
Therefore, y = 40.135 + 1.905x
To solve for x = 1
y = 40.135 + 1.905(1)
= 38.23
To solve for x = 8
y^ = 40.135 + 1.905(8)
= 55.375
Hence the answer is the values for x = 1, then y = 38.23 and for x = 8, then y^ = 55.375.
To learn more about expressions click here https://brainly.com/question/4344214
#SPJ9
Jay Field's bank granted him a single-payment loan of $6,800. He agreed to repay the loan in 91 days at an ordinary interest rate of 4.25 percent. What is the maturity value of the loan?
Answer:
$6,872.05
Explanation:
The maturity value of the loan can be calculated as:
[tex]V=P(1+r\cdot t_{})[/tex]Where P is the initial amount, r is the interest rate as a decimal and t is the time in years.
4.25% is equivalent to: 4.25/100 = 0.0425
91 days are equivalent to 91/365 = 0.25 years
Then, the maturity value is equal to:
[tex]\begin{gathered} V=6800(1+0.0425\cdot0.25) \\ V=6800(1+0.011) \\ V=6800(1.011) \\ V=\text{ \$6,872.05} \end{gathered}[/tex]So, the maturity value of the loan is $6,872.05
Question AA baseball is hit, following a path represented by x = 135t and y = 3.3 + 38t − 16t 2 for 0 ≤ t ≤ 3.Part A: Find the ordered pairs, (x, y) when t = 0.2, 1.2, and 2.2.Part B: The fence, which is 10 feet tall, lies 320 feet away from home plate. Does the baseball travel over the fence? Justify your answer mathematically.Part C: Write a rectangular equation to represent the plane curve.
Explanation
For the given question, we have the following
[tex]\begin{gathered} x=135t \\ y=3.3+38t-16t^2 \end{gathered}[/tex]Part A
find the ordered pairs (x,)
[tex]\begin{gathered} when \\ t=0.2 \\ \\ x=135(0.2)=27 \\ y=3.3+38(0.2)-16(0.2)^2=10.26 \\ \\ when\text{ t=0.2} \\ (x,y)=(27,10.26) \\ \end{gathered}[/tex][tex]\begin{gathered} when \\ t=1.2 \\ x=135(1.2)=162 \\ y=3.3+38(1.2)−16(1.2)^2=25.86 \\ \\ (x,y)=(162,25.86) \end{gathered}[/tex][tex]\begin{gathered} when \\ t=2.2 \\ x=135(2.2)=297 \\ y=3.3+38(2.2)−16(2.2)^2=9.46 \\ \\ (x,y)=(297,9.46) \end{gathered}[/tex]28 ft 20 it 18 ft Given x < 20, which COULD be the area of this trapezoid? 424 ft2 B) 460 +2 464 ft2 5042
Trapezoid area =(Base 1 + Base 2 )Height/2
If x= 20
then area = (28+18)/2 • √ ( 20^2 - 5^2)
. = 23 • √375
. = 445
If x< 20 ,area is
Answer is OPTION A ) 424 ft2
Write the following decimal numbers as a fraction: • One hundred and twenty four hundredths • Five tenths 5/10 Twenty seven thousandths Fifty two and nine hundredths
ANSWER:
10024/100
5/10
27/1000
5209/100
STEP-BY-STEP EXPLANATION:
The first thing is to convert the writing into a decimal number and then convert it into a fraction, just like this:
One hundred and twenty four hundredths:
100.24 = 10024/100
Five tenths
0.5 = 5/10
Twenty seven thousandths
0.027 = 27/1000
Fifty two and nine hundredths
52.09 = 5209/100
Use the Pythagorean Theorem to find the missi romanille 1 1 point a = 3 and b = 7. Round to two decimal places. Type your answer... 2. 1 point a = 3 and c = 23. Round to two decimal places. Type your answerExercise number 1
The formula of the Pythagorean Theorem is
[tex]\begin{gathered} a^2+b^2=c^2 \\ \text{ Where c is the hypotenuse and} \\ a,b\text{ are the sides of the triangle} \end{gathered}[/tex]Graphically,
So, in this case, you have
[tex]\begin{gathered} a=3 \\ b=7 \\ c=\text{?} \\ a^2+b^2=c^2 \\ \text{ Replacing} \\ (3)^2+(7)^2=c^2 \\ 9+49=c^2 \\ 58=c^2 \\ \text{ Apply square root to both sides of the equation} \\ \sqrt[]{58}=\sqrt[]{c^2} \\ 7.62=c \end{gathered}[/tex]Therefore, the missing side measurement is 7.62 units.
Find the surface area of a sphere with a radius of 1 cm to the nearest tenth. (Do NOTtypeinany units in your answer.)
The area of the sphere is 12.6
Here, we want to find the area of the sphere given the radius
Mathematically, we can calculate the area of the sphere using the formula below;
[tex]\begin{gathered} A\text{ = 4}\times\pi\times r^2 \\ r\text{ = 1 cm} \\ \pi\text{ = 3.142} \\ \text{Area of sphere = 4}\times3.142\times1^2=12.6cm^2 \end{gathered}[/tex]At his job, Tomas earns a commission plus an hourly wage. The function below describes the total dollar amount Tomas earns, based on the number of hours he works,f(h) = 250 +8.5hWhat represents the hourly rate Tomas earns
f(h) = 250 +8.5h
The function is on slope-intercept form:
y(x)= mx +b
Where m is the slope.
Rearranging the function given:
f(h) = 8.5h +250
Where:
250 is the fixed commission since it doesn't have a variable next to it.
8.5 is the hourly wage.
We can see that the hourly rate (8.5 per hour) is the slope of the function.
Turn into an inequality A speed limit of 65 mph
The question says we should turn into an inequality a speed limit of 65 miles per hour.
This means the speed should'nt be more than 65 miles per hour. In other words the speed shouldn't exceed 65 miles per hour.
Let represent the speed with a. Therefore,
a < 65 miles per hour
a < 65
Evaluate the expression when c = -3/10 and x = -7/8c + 1/5xWrite your answer in simplest form.
Explanation:
if c = -3/10 and x = -7/8
by replacing them in the equation c + 1/5 * x, we get:
[tex]\frac{-3}{10}+\frac{1}{5}*\frac{-7}{8}\text{ = }\frac{-3}{10}-\frac{7}{40}=\frac{-3*4}{10\text{ * 4}}-\frac{7}{40}=\text{ }\frac{-12-7}{40}\text{ = }\frac{-19}{40}[/tex]can someone please help me with question 3 and question 5-7
Question 5
The coordinate of C is (4,4)
If you dilate ABCD by a scale factor of 1/2, the coordinate of the image of C will be:
[tex]\begin{gathered} C^{\prime}(4\times\frac{1}{2},4\times\frac{1}{2}) \\ =(2,2) \end{gathered}[/tex]Question 6
The coordinate of A is (0,2)
If you dilate ABC by a scale factor of 2, the coordinate of the image of A will be:
[tex]\begin{gathered} A^{\prime}0\times2,2\times2) \\ =(0,4) \end{gathered}[/tex]