To solve this problem we can use the expression that defines percents. What price has a 75% of $90?
[tex]\text{Total}\cdot\frac{\text{percent}}{100}=\text{equivalent number to the percent}[/tex]With the information given, we know that the equivalent number to the percent is $90 and the percent is 75%.
Then, substitute and solve for the total variable:
[tex]\begin{gathered} \text{Total}\cdot\frac{75}{100}=90 \\ \text{Total}=\frac{90\cdot100}{75} \\ \text{Total}=120 \end{gathered}[/tex]The original price of the swing set is $120.
A swim team consist of seven boys and four girls a relay team of four swimmers is chosen at random from the team members what is the probability that three boys are selected for the relay team given that the first selection was a girl express your answer as a fraction in lowest terms or a decimal rounded to the nearest million
At start, we have:
- 7 boys
- 4 girls
It is given that the first selection was a girl. Since there were 4 girls, there is 3 left to be picked. So we have:
- 1 girl picked
- 7 boys to be picked
- 3 girls to be picked
We want the next 3 pickes to be boys.
The probability that the first pick will be a boy is the number of boys to be picked from over the total team left to be picked from. We have 7 boys and a total of 7 + 3 = 10 members, so:
[tex]P_1=\frac{7}{10}[/tex]Next, we want another pick of boy, but now we have got only
- 6 boys
- 3 girls
So, the probability of the second pick to be boy is:
[tex]P_2=\frac{6}{9}[/tex]And for the third, we have:
- 5 boys
- 3 girls
Probability of
[tex]P_3=\frac{5}{8}[/tex]Since we want these three to occur, the final probability is the product of them:
[tex]P=P_1\cdot P_2\cdot P_3=\frac{7}{10}\cdot\frac{6}{9}\cdot\frac{5}{8}=\frac{7}{1}\cdot\frac{1}{3}\cdot\frac{1}{8}=\frac{7}{24}[/tex]So, the answer as a fraction in the lowest form is:
[tex]\frac{7}{24}[/tex]17 * 7*20000000000000
Here, we want to multiply the given terms
The best way to go about this
Answer: 2.38e+15
Step-by-step explanation:
At the city museum, child admission is $5.90 and adult admission is $9.40. On Saturday, 170 tickets were sold for a total sales of $1332.00. How many adulttickets were sold that day?Number of adult tickets:
In this case, we'll have to carry out several steps to find the solution.
Step 01:
data:
city museum
Step 02:
system of equations:
x = # child tickets
y = # adult tickets
equations:
x + y = 170 eq. 1
5.90x + 9.40y = 1332 eq.2
x + y = 170 * (- 5.90)
5.90x + 9.40y = 1332
-5.90x - 5.90y = - 1003
5.90x + 9.40y = 1332
--------------------------------
3.5y = 329
y = 329 / 3.5
y = 94
The answer is:
# adult tickets = 94
Match the following items.1. (-14) + 81 = 81 + (-14)commutative property of addition312424 +. 15associative property of addition2.(24 + 15)3313 173.= 117 134. -72 + 0 = -72distributive propertymultiplicative inverse5. 101 + (29 +417) = (101 +29) + 417additive identity
The Solution.
1.
[tex](-14)+81=81+(-14)\text{ }\Rightarrow Commutative\text{ property of addition}[/tex]2.
[tex]\frac{1}{3}(24+15)=\frac{1}{3}.24+\frac{1}{3}.15\text{ }\Rightarrow\text{ Distributive property}[/tex]3.
[tex]\frac{13}{17}\times\frac{17}{13}=1\text{ }\Rightarrow Multiplicative\text{ inverse}[/tex]4.
[tex]-72+0=-72\text{ }\Rightarrow\text{ }Additive\text{ Identity}[/tex]5.
Countries represented at each festival 6 5 4 Number of festivals 3 N 1 0 0-5 6-11 12-17 18-23 24-29 Number of countries How many festivals had 12 or more countries represented.
11 festivals
Explanation
to find the nunmber of festivals that had 12 or more countries, sum the festivals for all values in number of countries greather than 12, it its
[tex]\begin{gathered} \text{column 3 (12-17)=5 festivals} \\ \text{column 4(18-23)=4 festivals} \\ column5(24-29)=2\text{ festivals} \\ so,\text{ the total of festivals for 12 or more countries is} \\ \text{total}=5+4+2 \\ total=11\text{ festivals} \end{gathered}[/tex]I hope this helps you
14. To surf the internet at the Airport costs $20,40 for 20 minutes and it costs $26.25 for 35minutes. How much would it cost to surf the internet for exactly 55 minutes.
Cost = $20.40 / 20 min
Cost = $26.25 / 35 min
To calculate the cost to suft 55 min just add the previous values given
Cost = 20.40 + 26.25
= $46.65
Suppose y = 6x −5. Find y if:x = −1/6y = ?
To find y, you can follow the steps:
Step 1: Substitute x by -1/6 in the equation.
[tex]\begin{gathered} y=-6x-5 \\ y=6\cdot(-\frac{1}{6})-5 \end{gathered}[/tex]Step 2: Solve the equation.
[tex]\begin{gathered} y=-\frac{6}{6}-5 \\ y=-1-5 \\ y=-6 \end{gathered}[/tex]Answer : y = -6.
I hope you are having a blessed day. Question is attached as a screenshot. Thank you :)
Solution:
Given the graphs of
[tex]\begin{gathered} y=x, \\ y=-x+4, \\ y=0 \end{gathered}[/tex]to be as plotted below:
The region ABC is bounded as shown above.
To find its area, the region ABC takes the shape of a triangle. Thus, we are to evaluate the area of the triangle ABC.
Step 1: Evaluate the midpoint between the distance AB.
The midpoint (x,y) of the distance AB is evaluated as
[tex]\begin{gathered} (x,y)=(\frac{x_1+x_2}{2},\frac{y_1+y_2}{2}) \\ \text{where} \\ x_1=0,y_1=0,x_2=2,y_2=2 \\ \text{thus,} \\ (x,y)=(\frac{0+2}{2},\frac{0+2}{2}) \\ =(1,1) \end{gathered}[/tex]Thus, the midpoint of the distance AB is (1,1).
Step 2: Evaluate the height of the region (triangle).
The height of the region is the same as the distance between points A and the midpoint of the distance AB.
Thus,
The distance is evaluated as
[tex]\begin{gathered} d=\sqrt[]{(x_2-x_1)^2+(y_2-y_1)^2} \\ \text{where} \\ x_1=2,y_1=2,x_2=1,y_2=1 \\ \text{thus,} \\ d=\sqrt[]{(1_{}-2_{})^2+(1_{}-2_{})^2} \\ =\sqrt[]{(-1_{})^2+(-1_{})^2} \\ =\sqrt[]{1+1} \\ d=\sqrt[]{2} \end{gathered}[/tex]Step 3: Evaluate the distance between points B and C.
The distance is evaluated similarly as
[tex]\begin{gathered} d=\sqrt[]{(x_2-x_1)^2+(y_2-y_1)^2} \\ \text{where} \\ x_1=0,y_1=0,x_2=4,y_2=0 \\ \text{thus,} \\ d=\sqrt[]{(4_{}-0_{})^2+(0_{}-0_{})^2} \\ =\sqrt[]{4^2+0^2} \\ d=4\text{ units} \end{gathered}[/tex]Step 4: Evaluate the area of the triangle ABC.
Given that the distance BC is 4 units and the height of the region is √2 units, the area of the region ABC is evaluated as the area of the triangle ABC.
Thus,
[tex]\begin{gathered} \text{Area = }\frac{1}{2}\times4\times\sqrt[]{2} \\ \Rightarrow Area\text{ =2}\sqrt[]{2} \end{gathered}[/tex]Hence, the area of the region is
[tex]2\sqrt[]{2}[/tex]The fourth option is the correct answer.
Rewrite the equation in standard form. Y+3=-(x-5)
To rewrite the given equation (point slope) into standard form:
1. Remove parentheses: Multiply each term in the parentheses by -1:
[tex]\begin{gathered} y+3=(-1)(x)+(-1)(-5) \\ \\ y+3=-x+5 \end{gathered}[/tex]2. Add x in both sides of the equation:
[tex]\begin{gathered} x+y+3=-x+x+5 \\ x+y+3=5 \end{gathered}[/tex]3. Subtract 3 in both sides of the equation:
[tex]\begin{gathered} x+y+3-3=5-3 \\ x+y=2 \end{gathered}[/tex]Then, the given equation in standard form is: x+y=210÷5+10-9×1110 / 5 + 10 - 9 * 11 equals what
Follow the order to solve polynomials
1. Powers and roots
2. Divisions and products
3. Sums and substractions
[tex]\begin{gathered} \frac{10}{5}+10-9\cdot11 \\ 2+10-99 \\ 12-99 \\ -87 \end{gathered}[/tex]The answer is -87
see attached for question and diagram
Given: D = (1,3) and E = (3,-3)
The graph of DE is as following:
a) Translation (0,2) then reflection on x-axis
So, at first move 2 units upward t hen reflect across x-axis
Note: the rule of reflection across x-axis: (x,y) to (x,-y)
the final result in green color
B) reflection in x-axis then clock wise rotation
(1,3) to (1,-3) to (-3 , -1)
(3,-3) to (3,3) to (3,-3)
Note : reflection cross x-axis will give the red dash line
Then make rotation for the red dash line will give the green line
What is the congruence correspondence, if any, that will prove the given triangles congruent?A. SASB. AASC. noneD. ASA
None (option C)
Explanation:Congruent triangles have same shape and size
Rules that can be used to prove triangle congruency:
SAS - side angel side
AAS = Angle angle Side
SSS = side-side-side
ASA = Angle-side-angle
From the triangles given, we see they are not of the same size even though they look alike.
Also the corresponding angles of both triangles do not look the same.
As a result, we do not have conguruence correspondence that will prove the triangles are congruent.
None
Which equations can you solve to find the value of m choose all that apply
m = 7.50 + 12.50
m - 7.50 = 12.50
Explanation:Cost of the book = $7.50
Amount remaining on the gift card = $12.50
m = Amount on the gift card in dollars when Salim received it
Amount on the gift card in dollars when Salim received it = Cost of the book + Amount remaining on the gift card
m = $7.50 + $12.50
m = 7.50 + 12.50
Another form of the equation:
subtract 7.5 from both sides:
m - 7.50 = 7.50 - 7.50 + 12.50
m - 7.50 = 12.50
Hence, equation that can be used to solve m:
m = 7.50 + 12.50
m - 7.50 = 12.50
If the spinner is spun, what is the probability that the spinner will land on a multiple of 4?
Answer: A
Step-by-step explanation:
There are 10 possible outcomes on the spinner listed 1-10.
The multiples of 4 are 4, 8, 12, 16, and so on.
On the spinner, there are only 4 and 8 (of the multiples), and out of the 10 outcomes, that's 2/10 of them both.
If you multiply that fraction by 10 (we multiply by 10 since 2/10 isn't on the answer choices, also a number over 100 is also a percent)
that gives us 20/100, or 20%.
Hope that helps!
which system of equations is better to start up to solve using the subsition method or the elemination method?
For the set of equations, the answer will be:
The elimination method is better because both equations are in general form.
A ball is thrown from an initial height of 3 meters with an initial upward velocity of 30 m/s. The ball’s height h (in meters) after t seconds is given by the following. h=3+30t-5t^2 Find all values of t for which the ball’s height is 13 meters. Round your answer(s) to the nearest hundredth.
Answer:
The values of t for which the ball's height is 13 meters is;
[tex]\begin{gathered} t=0.35\text{ s} \\ or \\ t=5.65\text{ s} \end{gathered}[/tex]Explanation:
The function of the ball's height h (in meters) is given as;
[tex]h=3+30t-5t^2[/tex]the value of time t for which the ball's height is 13 meters, can be derived by substituting h=13 into the function of h.
[tex]\begin{gathered} h=3+30t-5t^2 \\ 13=3+30t-5t^2 \\ 3+30t-5t^2=13 \end{gathered}[/tex]subtract 13 from both sides and solve the quadratic equation;
[tex]\begin{gathered} 3+30t-5t^2-13=13-13 \\ -5t^2+30t-10=0 \end{gathered}[/tex]solving the quadratic equation, using the quadratic formula;
[tex]\begin{gathered} t=\frac{-b\pm\sqrt{b^2-4ac}}{2a} \\ t=\frac{-30\pm\sqrt{30^2-4\times-5\times-10}}{2\times-5} \\ t=\frac{-30\pm\sqrt{900-200}}{-10} \\ t=\frac{-30\pm\sqrt{700}}{-10} \\ t=0.3542=0.35 \\ or \\ t=5.64575=5.65 \end{gathered}[/tex]The values of t for which the ball's height is 13 meters is;
[tex]\begin{gathered} t=0.35\text{ s} \\ or \\ t=5.65\text{ s} \end{gathered}[/tex]Find mZ1 in the picture below.1(3y² + 2y – 10)(2y² + 7y + 4)
m∠1=29
In this question,
1) Since we have, vertical angles, whose measure are written as polynomials then we can write according to the Vertical angles theorem:
3y² + 2y – 10 =2y² + 7y + 4
3y²-2y² -7y+2y-10-4=0
y²-5y-14=0
1.1) Finding the roots by Sum and Product
S(x) = ___ +___ = -5
P(x) =____ x ___ = -14
x1=-2 or 7
Since our Domain, cannot allow negative numbers, let's keep the positive one 7
2) Moreover to that, m∠1 + 2y² + 7y + 4 = 180º
m∠1 +2(7)²+7(7)+4=180
m∠1 +151 =180
m∠1=180-151
m∠1=29
Kelly is building a playpen for her dog. The area of the playpen is 22.75 square feet. The length is 6.5 feet and the width is w feet.
w = 3.5 feet
Explanation:Area = 22.75 square feet
length = 6.5 feet
width = w
Since we have beeen given dimensions in the form of length and width, the shape at the play house is a rectangle:
Area of rectangle = length × width
22.75 square feet = 6.5 feet × w
22.75 = 6.5w
divide both sides by 6.5:
22.75/6.5 = 6.5w/6.5
w = 3.5 feet
A survey of visitor at national park was conducted to determined the preferred activity. The survey results are shown in the table. Based on this information which prediction about the preferred activity for the next 200 visitors to the park is the most reasonable.
Given:
A survey of visitors at a national park is shown in the table.
a) The number of visitors who preferred champing is 28.
The number of visitors who preferred hiking tails is 22.
And The number of visitors who preferred champing is 6 more than visitors who preferred hiking tails.
Option a) is incorrect.
b) Hiking trails - water sports= 22-14=8
c) Water sports - biking trails = 14-16= -2
Option c) is incorrect.
d)
[tex]\begin{gathered} \text{Camping}=2\times water\text{ sports} \\ =2\times14 \\ =28 \end{gathered}[/tex]From the given options b) and d) shows the correct predictions.
Amoung these two options most reasonable is option d) for next 200 visitors.
If 9:x=x:4, then x = 3618246
Answer
Option D is correct.
x = 6
Explanation
9 : x = x : 4
To solve this, we know that ratios can be written in fraction form
(9/x) = (x/4)
[tex]\begin{gathered} \frac{9}{x}=\frac{x}{4} \\ \text{Cross multiply} \\ x^2=9\times4 \\ x^2=36 \end{gathered}[/tex]Take the square root of both sides
√(x²) = √(36)
x = 6
Hope this Helps!!!
What is the real part of 4 – 5i? 54-5i-5
Every imaginary number have the following form:
[tex]a\text{ +bi (1)}[/tex]Where a= real part , b= imaginary part
Basically on this case the real part would be the number without the i and the imaginary part the number with i
The real part is:
[tex]4[/tex]And the imaginary part:
[tex]-5[/tex]Final answer:
[tex]4[/tex]what is the lcm of 25 and 37?
SOLUTION:
Step 1:
In this question, we are meant to find the LCM of 25 and 37.
Step 2:
The least common multiple, lowest common multiple, or smallest common multiple of two integers a and b, usually denoted by lcm(a, b), is the smallest positive integer that is divisible by both a and b
Choose ALL answers that describe thequadrilateral DEFGit DE FG,EF | GD, diagonal DF = 16, and diagonalEG=16.
Having two sets of parallel lines means that it can either be a rectangle, a square, a parallelogram, or a rhombus.
Having the diagonals congruent makes this figure either a rectangle or a square.
Since the length of the side is not given, we can only assume that this is a rectangle.
Summarizing it all, quadrilateral DEFG is a parallogram that is a rectangle because of the two pairs of parallel lines, and it has congruent diagonals.
5. Solve the system of equations by graphing. y = -x + 2 3x + 3y = 6
Answer:
The system of equations has infinite number of solutions.
The solution to the system of equations is any point on the line of the graph.
Explanation:
Given the system of equations;
[tex]\begin{gathered} y=-x+2 \\ 3x+3y=6 \end{gathered}[/tex]Plotting the two equations using a graph calculator we have;
From the graph, we can observe that the line of the two equations fall on each other.
That means that the equations are the same.
Therefore, the system of equations has infinite number of solutions.
The solution to the system of equations is any point on the line of the graph.
Part 311Use the relationships in circle O to find the missing measures in circle S.1 pointIf WR = 12 units and MN = 8 units, determine MW.Type your answerwMRNePrestipus
From the properties of secant line and the tangent to the circle
If a secant segment and tangent segment are drawn to a circle from the same external point, the length of the tangent segment is the geometric mean between the length of the secant segment and the length of the external part of the secant segment.
[tex]\frac{Whole\text{ Secant}}{\tan gent\text{ Line}}=\frac{\tan gent}{External\text{ Secant Part}}[/tex]
In the given figure we hvae :
Whole secant length (RM),
Tangnt line MN = 8 units
External secant part (WM)
Since RM = WR + WM
RM=12 + WM
Susbtitute the value:
[tex]\begin{gathered} \frac{Whole\text{ Secant}}{\tan gent\text{ Line}}=\frac{\tan gent}{External\text{ Secant Part}} \\ \frac{RM}{MN}=\frac{MN}{MW} \\ \frac{12+MW}{8}=\frac{8}{MW} \\ \text{Apply crossmultiplication:} \\ MW(12+MW)=8\times8 \\ 12MW+(MW)^2=64 \\ \text{ Let MW = x} \\ 12x+x^2=64 \\ x^2+12x-64=0 \\ \text{ Factorize:} \\ x^2+16x-4x-64=0 \\ x(x+16)-4(x+16)=0 \\ (x-4)(x+16)=0 \\ \text{ So, x = 4, -16} \\ \text{ Since measurement cannot be negative thus: x = 4 unit} \\ x\text{ = }MW=4 \end{gathered}[/tex]Answer : MW= 4 units
7. Translate the following Marco has $6 less than Ann has
Solution:
Let x represent the amount Marco has,
let y represent the amount Ann has.
Given that Marcos has $6 less than Ann has, this implies that
[tex]\begin{gathered} x=y-6 \\ \end{gathered}[/tex]Ann has
[tex]y[/tex]Marco has
[tex]y-6[/tex]What are the leading coefficient and degree of the polynomial?-8u^6-15+4u+18u^9
The degree of a polynomial is given by the higher exponent of the variable.
In this polynomial, we have terms with the variable with exponents 6, 0, 1 and 9.
Therefore the degree of the polynomial is 9.
The leading coefficient is the number that multiplies the variable with a higher exponent.
The leading term is 18u^9, so the leading coefficient is 18.
Look at the graph of f(x). Which of the following are true? Select all that apply. 2 answers
Answer:
Explanation:
Answer:
A. [tex]f(x)[/tex] is [tex]y=sec(x-\pi )[/tex] shifted 6 units up.
C. [tex]f(x)[/tex] is [tex]y=sec(x)+6[/tex] shifted [tex]\pi[/tex] units to the left.
Step-by-step explanation:
If you guessed the answer to this question, or did not answer, go back and review how to write to equation of a trigonometric function.
Your welcome...
Use the sample data and confidence level given below to complete parts (a) through (d)A research institute poll asked respondents if they felt vulnerable to identity theft. In the poll, n = 1047 and x = 545 whosaid "yes." Use a 95% confidence level.A. find the best point of estimate of the population of portion p.B. Identify the value of the margin of error E. (E= round to four decimal places as needed.)C. Construct the confidence interval. (
a. The best point of estimate of the population of portion p is given by the formula:
[tex]p^{\prime}=\frac{x}{n}[/tex]where x is the number of successes x=545 and n is the sample n=1047.
Replace these values in the formula and find p:
[tex]p^{\prime}=\frac{545}{1047}=0.521[/tex]b. The value of the margin of error E is given by the following formula:
[tex]E=(z_{\alpha/2})\cdot(\sqrt[]{\frac{p^{\prime}q^{\prime}}{n}})[/tex]Where z is the z-score at the alfa divided by 2, q'=1-p'.
As the confidence level is 95%=0.95, then alfa is 1-0.95=0.05, and alfa/2=0.025
The z-score at 0.025 is 1.96.
Replace the known values in the formula and solve for E:
[tex]\begin{gathered} E=1.96\cdot\sqrt[]{\frac{0.521\cdot(1-0.521)}{1047}} \\ E=1.96\cdot\sqrt[]{\frac{0.521\cdot0.479}{1047}} \\ E=1.96\cdot\sqrt[]{\frac{0.2496}{1047}} \\ E=1.96\cdot\sqrt[]{0.0002} \\ E=1.96\cdot0.0154 \\ E=0.0303 \end{gathered}[/tex]c. The confidence interval is then:
[tex]\begin{gathered} (p^{\prime}-E,p^{\prime}+E)=(0.521-0.0303,0.521+0.0303) \\ \text{Confidence interval=}(0.490,0.551) \end{gathered}[/tex]d. We estimate with a 95% confidence that between 49% and 55.1% of the people felt vulnerable to identity theft.
Precalculus:Consider the right triangle where a = 3mi and alpha = 45 degrees Find an approximate value (accurate up to three or more decimals) of each of the following. Give the angle in degrees.
Given:
[tex]\begin{gathered} a=3mi \\ \alpha=45\degree \end{gathered}[/tex]Required:
To find the value of beta, b and c.
Explanation:
The given triangle is right triangle.
Therefore,
[tex]\begin{gathered} \sin\alpha=\frac{a}{c} \\ \\ \sin45=\frac{3}{c} \\ \\ 0.7071=\frac{3}{c} \\ \\ c=\frac{3}{0.7071} \\ \\ c=4.2426mi \end{gathered}[/tex]Now
[tex]\begin{gathered} \tan\alpha=\frac{a}{b} \\ \\ \tan45=\frac{3}{b} \\ \\ 1=\frac{3}{b} \\ \\ b=3 \end{gathered}[/tex]The sum of the angle in triangle is 180 degree.
Therefore
[tex]\begin{gathered} 90+45+\beta=180 \\ \beta=180-90-45 \\ \beta=45\degree \end{gathered}[/tex]Final Answer:
[tex]\begin{gathered} b=3mi \\ c=4.2426mi \\ \beta=45\degree \end{gathered}[/tex]