The dilation factor is 2/3. So ratio of sides of triangle is,
[tex]\frac{U^{\prime}S^{\prime}}{US^{}}=\frac{2}{3}[/tex]Determine the length of side US.
[tex]\begin{gathered} \frac{20}{US}=\frac{2}{3} \\ US=20\cdot\frac{3}{2} \\ =30 \end{gathered}[/tex]So measure of side US is 30 units.
17. How many solutions does thesystem of equations have?4x + 5y = 65y + 4x = 8A one solutionB) two solutionsC infinitely many solutionsno solution
we have the following:
[tex]\begin{gathered} 4x+5y=6 \\ 5y+4x=8 \end{gathered}[/tex]solving:
[tex]\begin{gathered} 4x+5y=6 \\ x=\frac{6-5y}{4} \end{gathered}[/tex]replacing:
[tex]\begin{gathered} 5y+4\cdot\frac{6-5y}{4}=8 \\ 5y+6-5y=8 \\ 6=8 \end{gathered}[/tex]therefore, the system no solutions
Simplify the ratio 15 to 21 is?
Given the ratio;
[tex]15\colon21[/tex]To simplify the above ratio, we would change the ratio to a fraction then divide the numerator and the denominator by the same value, and till we get to the lowest possible term.
This gives,
[tex]\begin{gathered} \frac{15}{21}\mleft\lbrace\text{Divide numerator and denominator by 3}\mright\rbrace \\ =\frac{5}{7} \\ \therefore5\colon7 \end{gathered}[/tex]Therefore, the answer is
Answer: 5:7
Which of the following is equal to √500? 5010√5010√550√105√10
You can use the product property of square roots:
[tex]\sqrt[]{a\cdot b}=\sqrt[]{a}\cdot\sqrt[]{b}[/tex]Also, you can express 500 as the product of 100*5, then
[tex]\begin{gathered} \sqrt[]{500}=\sqrt[]{100\cdot5}\text{ appling the product property} \\ \sqrt[]{100\cdot5}=\sqrt[]{100}\cdot\sqrt[]{5}\text{ and the square root of 100 is 10, then} \\ \sqrt[]{100}\cdot\sqrt[]{5}=10\cdot\sqrt[]{5} \end{gathered}[/tex]The answer is 10√5
JK bisects angle LJM, the measure of angle LJM=2x+15, and the measure of angle KJM=6x-5. Solve for x.
JK bisects angle LJM, the measure of angle LJM=2x+15, and the measure of angle KJM=6x-5. Solve for x.
In this problem we have that
because JK bisects angle LJM
substitute the given values
(2x+15)=2(6x-5)
solve for x
2x+15=12x-10
12x-2x=15+10
10x=25
x=25/10
x=2.5Can I please get help on this question I guessed it and I got it right. But I would like to know the solution to this.
Remember that, the Confidence Interval is a range of estimates defined by a lower bound and an upper bound. The larger the percentage of the confidence interval is, the more data the CI range includes.
Therefore, the 95% interval contains more data than the 90% confidence interval. Then, the answer is always narrower.
Solve the following system of equations using elimination. A. (4, 2)B. (2, 16)C. (-2, 16)D. (16, -2)
Answer:
A. (4, 2)
Explanation:
Given the system of equations:
[tex]\begin{gathered} x+3y=10\cdots(1) \\ 6x+12y=48\cdots(2) \end{gathered}[/tex]In order to use the elimination method, multiply the first equation by 6 to make the coefficients of x the same.
[tex]\begin{gathered} 6x+18y=60\cdots(3) \\ 6x+12y=48\cdots(2) \end{gathered}[/tex]Subtract equation (2) from equation (3).
[tex]\begin{gathered} 6y=12 \\ \text{Divide both sides by 6} \\ y=\frac{12}{6} \\ y=2 \end{gathered}[/tex]Next, solve for x using any of the equations:
[tex]\begin{gathered} x+3y=10 \\ x+3(2)=10 \\ x=10-6 \\ x=4 \end{gathered}[/tex]The solution to the system of equations is (x,y)=(4,2).
Option A is correct.
I just need the answer
Answer
(x - 3) and (x - 8)
Explanation:
The root of the equation is 3 and 8
(x - 3) = 0 or (x - 8) = 0
(x - 3) (x - 8) = 0
Therefore, the zero of the quadratic function are (x - 3) and (x - 8)
Math scores for two classes are shown in the box plot below. A. What is the median score of class AB. What is the interquartile range of class B?See question and box plot in attached photo.
Let's put more details in the given question to better understand the problem:
Let's now answer the questions:
A. What is the median score of class A?
Based on the given box plot, the median score of Class A is 73.
The answer is 73.
B. What is the interquartile range of class B?
For us to get the interquartile range, we will be using the following formula:
[tex]\text{ Interquartile range = Q}_3\text{ - Q}_1[/tex]In the given box plot for Class B, the following are observed:
Q3 = 87
Q1 = 79
Therefore, the interquartile range will be:
[tex]\text{ Interquartile range = 87 - 79 = 8}[/tex]The interquartile range of Class B is 8.
The answer is 8.
A group of friends shook hands with each other at a party. Peter did notshake hands with everyone at the party because he was late and somefriends had already left. There were a total of 25 handshakes. How many friends were still at the party when Peter arrived?
When "n" number of people then number of people is:
[tex]\text{handshakes}=\frac{n(n-1)}{2}[/tex]If the handshakes is 25 then:
[tex]25=\frac{n(n-1)}{2}[/tex][tex]\begin{gathered} 25\times2=n(n-1) \\ 50=n^2-n \\ n^2-n-50=0 \\ \end{gathered}[/tex]Solve the equation:
[tex]\begin{gathered} n=\frac{-(-1)\pm\sqrt[]{1-4(1)(-50)}}{2} \\ n=\frac{1\pm\sqrt[]{1+200}}{2} \\ n\approx7 \end{gathered}[/tex]So 7 friends still at the party.
A man purchased a magazine at the airport for $2.39. The tax on the purchase was $0.17. What is the tax rate at the airport? Raund to the nearest percentThe tax rate is ? Round to the nearest percent as needed.
In order to find the percent corresponding to the tax rate, we divide the tax over the cost of the magazine and multiply it by 100
[tex]\frac{0.17}{2..39}\cdot100=7.11\text{\%}\approx7\text{\%}[/tex]While value of x is a solution to this equation? 5x^2-36x+36=0A. x=-6B. x=4C. x=-1.8D. x=1.2
Answer:
D. x = 1.2
Explanation:
A value of x is a solution of the equation if when we replace, x by the given value, the equation is satisfied.
Therefore, for each option we get:
A. Replacing x = -6, we get:
5x² - 36x + 36 = 0
5(-6)² - 36(-6) + 36 ≠ 0
5(36) + 216 + 36 ≠ 0
180 + 216 + 36 ≠ 0
432 ≠ 0
Then, x = -6 is not a solution of the equation
B. Replacing x = 4, we get:
5x² - 36x + 36 = 0
5(4)² - 36(4) + 36 ≠ 0
5(16) - 144 + 36 ≠ 0
80 - 144 + 36 ≠ 0
-28 ≠ 0
Then, x = 4 is not a solution of the equation
C. Replacing x = -1.8, we get:
5x² - 36x + 36 = 0
5(-1.8)² - 36(-1.8) + 36 ≠ 0
5(3.24) + 64.8 + 36 ≠ 0
16.2 + 64.8 + 36 ≠ 0
117 ≠ 0
Then, x = -1.8 is not a solution of the equation
D. Replacing x = 1.2, we get:
5x² - 36x + 36 = 0
5(1.2)² - 36(1.2) + 36 = 0
5(1.44) - 43.2 + 36 = 0
7.2 - 43.2 + 36 = 0
0 = 0
Then, x = 1.2 is a solution of the equation
Therefore, the answer is x = 1.2
Last year Brian opened an investment account with $5800. At the end of the year, the amount in the account had increased by 24.5%. How much is this increased in dollars? How much money was in his account at the end of last year?
Part a
How much is this increased in dollars?
Remember that
24.5%=24.5/100=0.245
so
Multiply the initial amount by the factor of 0.245, to obtain how much is increased
$5,800*0.245=$1,421
the answer part a is $1,421Part b
How much money was in his account at the end of last year?
Adds $5,800 and $1,421
$5,800+$1,421=$7,221
the answer part b is $7,22114.9x+1/3 (-12-27x)-33.2 , x=-3simplify the expression using the properties of operations.
14.9x+1/3 (-12-27x)-33.2
Using PEDMAS;
First, let's open the parenthesis
14.9x - 4 - 9x - 33.2
Rearrange
14.9x - 9x -4 -33.2
5.9x - 37.2
But from the question x= -3
Substitute x=-3 in the above;
5.9(-3) - 37.2
-17.7 - 37.2
-54.9
The diagonales of this rhombus are 20 millimeters and 7 millimeters.
The rule of the area of the rhombus using its 2 diagonals is
[tex]A=\frac{d1\times d2}{2}[/tex]Since the diagonals of the given rhombus are 20 mm and 7 mm
Then d1 = 20 and d2 = 7
Substitute them in the rule above
[tex]\begin{gathered} A=\frac{20\times7}{2} \\ A=\frac{140}{2} \\ A=70mm^2 \end{gathered}[/tex]The area of the rhombus is 70 square millimeters
Simplify.4(7d+9)28d + 3628d + 911d + 1311d + 9
To simplify the above expression, simply distribute "4" or multiply it to the numbers inside the parenthesis.
[tex]\begin{gathered} (4\times7d)+(4\times9) \\ 28d+36 \end{gathered}[/tex]Hence, the answer is 28d + 36.
It’s a bit easy but I just need to know the answer
The given function is,
[tex]g(x)=x^3+2[/tex]The parent function is,
[tex]f(x)=x^3[/tex]The graph of the function and the parent function can be drawn as,
Where red graph is the parent function f(x) and the blue graph is given by the function g(x).
From the graph it is evident that the g(x) is the translation of the graph f(x) by 2 units up.
Thus, "2 units" and "up" are the correct options.
a surveyor standing 58 M from the base of a building measures the angle to the top of the building and finds it to be 39 degrees. the surveyor then measures the angle to the top of the radio tower on the building and find that it is 48°. how tall is the radio tower .
First, let's calculate the height to the top of the building:
Thereby,
[tex]\begin{gathered} \tan 39=\frac{B}{58}\rightarrow B=58\tan 39 \\ \Rightarrow B=46.97m \end{gathered}[/tex]Now, let's calculate the height to the top of the radio tower:
This way,
[tex]\begin{gathered} \tan 48=\frac{T}{58}\rightarrow T=58\tan 48 \\ \Rightarrow T=64.42 \end{gathered}[/tex]Substracting both heights, we'll get that:
[tex]64.42-46.97=17.45[/tex]The radio tower is 17.45 m tall.
In a game, two fair number cubes with faces numbered 1 through 6 are rolled. If the sum of the two numbers rolled is 12, the player wins c coupons. 11, the player wins 4 coupons. less than 11, the player loses 2 coupons. What value of c makes this game fair? A.10B.14 C.58 D.64
the probability to get a number less than 11 is 33/36, to get an 11 is 2/36 and to get an 12 is 1/36. if we want the game to be fair, the expected value should be 0, so we get
[tex]-2\cdot\frac{33}{36}+4\cdot\frac{2}{36}+\frac{c}{36}=0\rightarrow-66+8+c=0\rightarrow c=66-8=58[/tex]Write the equation 16x2 + 25y2 − 32x + 50y + 16 = 0 in vertex form.
Solution
We have the following equation given:
[tex]16x^2+25y^2-32x+50y+16=0[/tex]We can complte the squares and we have this:
[tex]16(x^2-2x)+25(y^2+2y)+16=0[/tex][tex]16(x^2-2x+1)+25(y^2+2y+1)+16=16+25[/tex]And then if we simplify we got:
[tex]16(x-1)^2+25(y+1)^2=25[/tex][tex]\frac{(x+1)^2}{(\frac{5}{4})^2}+\frac{(y+1)^2}{1}=1[/tex]Using the formula for area of a rectangle, A = lw, solvefor the length, l.
ANSWER
[tex]l=\frac{A}{w}[/tex]EXPLANATION
We want to solve for the length, l, in the formula for the area of a rectangle:
[tex]A=lw[/tex]We simply want to make the length the subject of the formula. To do this, divide both sides of the formula by w:
[tex]\begin{gathered} \frac{A}{w}=\frac{lw}{w} \\ \Rightarrow l=\frac{A}{w} \end{gathered}[/tex]That is the answer.
Identify the mathematical properties Liam uses to justify each step
Given the following expression:
[tex]\text{ 2x(x + 3) = 6x + 4}[/tex]Let's determine the mathematical properties being used as we simplify,
Step 1: Distributive Property
[tex]\text{ 2x(x + 3) = 6x + 4}[/tex][tex]\text{ (2x)(x)+ (2x)(3) = 6x + 4}[/tex][tex]\text{ 2x}^2\text{ + 6x = 6x + 4}[/tex]Step 2: Subtraction Property of Equality.
[tex]\text{ 2x}^2\text{ + 6x = 6x + 4}[/tex][tex]\text{ 2x}^2\text{ + 6x - 6x = 6x -6x + 4}[/tex][tex]\text{ 2x}^2\text{ = 4}[/tex]Step 3: Division Propert
At the produce store you can buy 2 bags of bananas for $13.90. How muchwould it cost if you were to buy 7 bags?
ANSWER:
$ 48.65
STEP-BY-STEP EXPLANATION:
We can calculate the value of 7 bags with the help of the following proportion:
[tex]\frac{13.9}{2}=\frac{x}{7}[/tex]We solve for x, which would be the cost of the 7 bags, like this:
[tex]\begin{gathered} 13.9\cdot7=2\cdot x \\ x=\frac{97.3}{2} \\ x=48.65 \end{gathered}[/tex]The cost of 7 bags is $ 48.65
The probability that a customer will order a nonalcoholic beverage is .48b. Find the probability that in a sample of 12 customers, at least 5 will order a nonalcoholic beverage. (Round your answer to 4decimal places.)
Given:
probability of ordering non-alcoholic beverage = 0.48
probability of not ordering non-alcoholic beverage = 1 - 0.48 = 0.52
FInd: the probability that in a sample of 12 customers, at least 5 will order a nonalcoholic beverage.
Solution:
Recall the binomial probability formula.
[tex]P(x)=nCr\times p^r\times q^{n-r}[/tex]where
p = probability of success: 0.48
q = probability of failure: 0.52
n = the number of samples: 12
r = number of success (at least 5 which means not 1, 2, 3, or 4.
To determine the probability of having at least 5, let's calculate when r = 0, r = 1, r = 2, r = 3, and r = 4.
Let's start with r = 0 and solve.
[tex]P(0)=_{12}C_0\times0.48^0\times0.52^{12}[/tex][tex]\begin{gathered} P(0)=1\times1\times0.000390877 \\ P(0)=0.000390877 \end{gathered}[/tex]At r = 1,
[tex]P(1)=_{12}C_1\times0.48^1\times0.52^{11}[/tex][tex]\begin{gathered} P(1)=12\times0.48^\times0.000751686 \\ P(1)=0.0043297 \end{gathered}[/tex]Now, let's solve for r = 2.
[tex]P(2)=_{12}C_2\times.48^2\times.52^{10}[/tex][tex]\begin{gathered} P(2)=66\times.2304\times.00144555 \\ P(2)=0.02198 \end{gathered}[/tex]Moving on to r = 3.
[tex]P(3)=_{12}C_3\times0.48^3\times0.52^9[/tex][tex]\begin{gathered} P(3)=220\times0.110592\times0.0027799 \\ P(3)=0.067636 \end{gathered}[/tex]Then, lastly at r = 4.
[tex]P(4)=_{12}C_4\times0.48^4\times0.52^8[/tex][tex]\begin{gathered} P(4)=495\times0.05308\times0.00534597 \\ P(4)=0.14047 \end{gathered}[/tex]Let's now add the probability of getting r = 0, r = 1, r = 2, r =3, and r = 4 customers ordering a nonalcoholic beverage.
[tex]P(0)+P(1)+P(2)+P(3)+P(4)[/tex][tex]0.0043297+0.02198+0.067636+0.14047=0.2344157[/tex][tex]0.000390877+0.0043297+0.02198+0.067636+0.14047=0.2348[/tex]0.2348 is the probability of at most 4 customers ordering a non-alcoholic beverage.
Since the question is the probability of at least 5 customers ordering a non-alcoholic beverage which is the opposite of the at most 4 customers, then, let's subtract its probability from 1.
[tex]1-0.2348=0.7652[/tex]Therefore, the probability that in a sample of 12 customers, at least 5 will order a nonalcoholic beverage is approximately 0.7652.
Write 0.611111111111 as a fraction PLEASE EXPLAIN STEP BY STEP!
We have to write N=0.6111... as a fraction.
This is a periodic number.
We start by transforming the number as:
[tex]10\cdot N=10\cdot0.6111\ldots=6.111\ldots=6+0.111\ldots[/tex]Now we take the periodic part we have (x=0.111...) and express it like this:
[tex]10x=10\cdot0.111\ldots=1.111\ldots=1+0.111\ldots=1+x[/tex]Then, we have:
[tex]\begin{gathered} 10x=1+x \\ 10x-x=1 \\ 9x=1 \\ x=\frac{1}{9} \end{gathered}[/tex]We use 10 to have the non-periodic part as an integer and the periodic part as a decimal.
Now we know that our periodic part of the number is equal to 1/9.
So we come back to N and complete:
[tex]\begin{gathered} 10N=6+0.111\ldots=6+\frac{1}{9} \\ N=\frac{1}{10}(6+\frac{1}{9})=\frac{1}{10}(\frac{6\cdot9}{9}+\frac{1}{9})=\frac{1}{10}\cdot\frac{54+1}{9}=\frac{1}{10}\cdot\frac{55}{9}=\frac{55}{90} \end{gathered}[/tex]Then, 0.6111... as a fraction is 55/90.
The lengths of two sides of an isosceles triangle are 5 and 9. The length of the third side could beA. 9, onlyB. none of theseC. either 5 or 9D. 5, only
Step 1: Theorem
In geometry, an isosceles triangle is a triangle that has two sides of equal length.
Step 2: Given data
Two sides are given with lengths 5 and 9.
Step 3:
The two equal lengths can be 5 and 5 or 9 and 9
Step 4:
The third length can be 5 or 9.
Final answer
is either 5 or 9.
This probability distribution shows thetypical distribution of the number of shoes
First, add the frequencies in order to obtain the total number of surveyed people,
[tex]T=12+20+38+20+10=100[/tex]Then, the condition 'a teenager has 4 or more pairs of shoes' is satisfied if the number of shoes is either 4 or 5; then,
[tex]P(4or5)=P(4)+P(5)=\frac{20}{100}+\frac{10}{100}=\frac{30}{100}=\frac{3}{10}[/tex]The exact answer is 3/10 or 0.3 (both are equivalent)Given the following table with selected values of f (x) and g(x), evaluate f (g(1)).x–6–4134f (x)4–1–613g(x)143–4–6A. –4B.–1C.1 D.4
[tex]f[g(1)][/tex]
The function is a composite function
Let us first find g(1)
[tex]g(1)=3[/tex]The problem now reduces to f(3)
[tex]f(3)=1[/tex]The final answer is 1 .
The right choice is OPTION C
In a survey of 29 instructors, it was found that 22 liked white boards, 11 liked blackboards, and 7 liked both. How many instructors did not like white boards?
We need to find the number of instructors that did not like whiteboards.
In order to do so, notice that from the 11 instructors who liked blackboards, 7 also liked whiteboards.
Thus, among the instructors who liked at least one of the two types of boards, the number of them who didn't like whiteboards is:
[tex]11-7=4[/tex]Also, there were some instructors among the whole group of 29 that didn't like any of the two boards. Thus, those ones didn't like whiteboards.
The following image illustrates this problem:
So, we need to find x and add it to the other 4 instructors that didn't like whiteboards.
We have:
[tex]\begin{gathered} 15+7+4+x=29 \\ \\ 26+x=29 \\ \\ x=29-26 \\ \\ x=3 \end{gathered}[/tex]Thus, another 3 instructors didn't like whiteboards.
Therefore, the total number of instructors who didn't like whiteboards is
[tex]4+3=7[/tex]Notice that we can find the same result in a faster way: since 22 instructors liked whiteboards from a total of 29 instructors, it means that 29 - 22 = 7 didn't like whiteboards.
Therefore, the answer is 7.
At the fair 220 balloons are given to 40 children, 3/4 of whom are girls. Each boy receives twice as many balloons as each girl. How many more balloons do all the girl receive than all the boys
We have the following:
3/4 of 40 = 30 girls, therefore 10 boys
Due each boy receives twice as many balloons as each girl
boys get a multiple of 20 balloons (10 * 2), girls get the same multiple of 30 (30 * 1) balloons.
so
x * (30 + 20) = 220 balloons
x * 50 = 220 balloons
x = 220/50
so the number is 4.4
Boys receive 20 * 4.4 = 88 balloons.
Girls receive 30 * 4.4 = 132 balloons.
(a) Explain how the number of standard deviations could be found for any data set. Choose the correct answer below.(b) Find the number of standard deviations
The Empirical Rule states that:
• about 68% of values fall within one standard deviation of the mean,,
,• about 95% of the values fall within two standard deviations from the mean,
,• almost all of the values—about 99.7%—fall within three standard deviations from the mean.
According to this, to have at least 99.0% of the data inside our interval, we must select approximately k = 3 standard deviations.
Answer• A. Use the Empirical Rule
,• k = 3