Answer
Explanation:
The symbol for percentage % means that the number is divided by 100. It means that 12% is equivalent to:
[tex]12\text{ \% = }\frac{12}{100}=0.12[/tex]Therefore, the decimal number that represents the percentage of students going on the trip is 0.12
I need help with this please! This is for Geometry :)
I need help on this question, I can’t figure this out, the whole thing.
Definitions in Statistics
We are given a list of examples and the second list of stats vocabulary. It's required to match them up.
* All people who drive on Highway 50
This corresponds to all the possible samples that can be taken in the study, thus it must be matched with e. Population
* The speed that a driver drives on Highway 50
From all the possible features we could observe, we select one of them. This feature is called the variable. a. Variable
* The average speed that the 250 randomly selected drivers drove on Highway 50
All the dataset is represented by a single number. This is called a parameter. d. Parameter
* The list of the 250 speeds that the drivers studied drove
All the speeds obtained in the study correspond to the Dataset, or simply the data. c. Data
* The 250 randomly selected drivers who were on Highway 50
From the population, only a portion was selected for the study. This corresponds to the sample. b. Sample
* The average speed that all drivers go on Highway 50
The main feature being measured and that justifies the whole study is the statistic. f. Statistic
RATIOS, PROPORTIONS, AND PERCENTSCalculating income taxBob made $6000 in taxable income last year.Suppose the income tax rate is 15% for the first $9000 plus 17% for the amount over $9000.How much must Bob pay in income tax for last year?I need help with this math problem.
Solution:
Given that the taxable income made last year was $6000.
Then, the income tax Bob paid for last year is;
[tex]0.15\times6000=900[/tex]ANSWER: $900
6. A four-ounce serving of orange juice contains 50 calories. About how many calories are in a 14-ounce glassof orange juiceA. I calB. 14 calC. 175 calD. 700 cal
SOLUTION
A 4 - ounce of orange juice contains 50 calories.
This means that 1 - ounce of orange juice will contain
[tex]\frac{1}{4}\times50\text{ = 12.5 calories }[/tex]Therefore, 14 - ounce will contain 14 x 1 - ounce
[tex]\begin{gathered} =\text{ 14}\times12.5\text{ } \\ =\text{ 175 calories } \end{gathered}[/tex]Therefore, the correct answer is option C. 175 cal
While Shopping Margaret bought a total of 10 items ( pants and t shirts) each pair of pants cost $53, each shirt is $27. She spent $374. How many pants and How many shirts.
Given that she bought a total of 10 items ( pants and t-shirts) each pair of pants cost $53, each shirt is $27. She spent $374, we have two linear equations as follows:
Let x be the number of pants and let y be the number of t-shirts, then:
[tex]53x+27y=374[/tex][tex]x+y=10[/tex]In order to find how many and shirts she bought, we have to solve this linear system of two equations and two variables:
[tex]53x+27y=374\rightarrow53x=374-27y\rightarrow x=\frac{374-27y}{53}[/tex][tex]\mathrm{Substitut}e\mathrm{\:}x=\frac{374-27y}{53}\text{ }into\text{ x + y = 10}[/tex][tex]\frac{374-27y}{53}+y=10[/tex][tex]\frac{374+26y}{53}=10[/tex][tex]\mathrm{Isolate}\:y[/tex][tex]\frac{53\left(374+26y\right)}{53}=10\cdot \:53[/tex][tex]374+26y=530[/tex][tex]374+26y-374=530-374\rightarrow26y=156\rightarrow y=6[/tex]then:
[tex]x=10-y=10-6=4[/tex]So, she bought 4 pants and 6 t-shirts.
I need help with this now. She said that we were supposed to solve for the area of the composite structures inside the structures.
We can decompose the figure in structures such that we can calculate the area of each structure.
Then, we have 3 rectangles, two triangles and a semicircle. The semicircle has diameter equals to
[tex]\begin{gathered} d=43ft-10ft-9ft=24ft \\ \end{gathered}[/tex]Then, the radius is equal to r=12ft.
We divide the figure in 6 different structures:
Structures I and V are triangles, so their area is
[tex]\frac{b\times h}{2}[/tex]Structures II, III and IV are rectangles, so their area is
[tex]a\times b\text{.}[/tex]Structure VI is a semicircle, so the area is
[tex]\frac{\pi r^2}{2}\text{.}[/tex]All the areas are in squared feet.
Structure I (b=10, h=48-37=11)
[tex]\frac{10\times11}{2}=55[/tex]Structure II (a=37, b-10)
[tex]37\times10=370[/tex]Structure III (a=38-12=26, b=43-10-9=24)
[tex]26\times24=624[/tex]Structure IV (a=32, b=9)
[tex]32\times9=288[/tex]Structure V (b=9, h=40-32=8)
[tex]\frac{9\times8}{2}=36[/tex]Structure VI (r=12)
[tex]\frac{(3.14)(12)^2}{2}=226.08[/tex]Then, we can obtain the total area adding all the area of the structures.
[tex]55+370+624+288+36+226.08=1599.08[/tex]So, the total area is 1599.08 squared feet.
Write a system of equations to describe the situation below, solve using any method, and fill in the blanks. Reid wants to make scrapbooks with old family photos. An online scrapbooking company charges $46 for a basic book and $1 per page. Meanwhile, a family friend is willing to make a scrapbook for $34 plus $3 per page. For a certain number of pages, the price would be equal. How many pages would that be? How much would that cost? If the scrapbook had blank pages, it would cost $blank
Let p be the number of pages printed.
The expression for the price charged by the online scrapbooking company is:
[tex]46+p[/tex]And the expression for the price charged by the family friend is:
[tex]34+3p[/tex]SInce both prices will be the same for a certain value of p, we'll get that
[tex]46+p=34+3p[/tex]Solving for p :
[tex]\begin{gathered} 46+p=34+3p \\ \rightarrow46-34=3p-p \\ \rightarrow12=2p \\ \rightarrow6=p \end{gathered}[/tex]This way, we can conclude that both prices will be the same for 6 pages.
This price would be:
[tex]\begin{gathered} 46+p\rightarrow46+6\rightarrow52 \\ 34+3p\rightarrow34+3(6)\rightarrow52 \end{gathered}[/tex]$52
Hi I need help to make sure I'm answering this question right
Firstly, we are going to plot the given on a graph sheet.
The inequalities sign would be reverse. This is to ensure we have a clearer to ascertain where the solutions
This is shown in the image below:
The points that fall on the unshaded part of the graph are the solutions to the system of inequalities and these points are (-1,8) and (1,5).
Hence, the correct options are E and F
2 1/2 : 3 1/2 = n:2what do the : between numbers mean?
The symbol : denotes that the two ratios are in proportion
[tex]\begin{gathered} 2\frac{1}{2}\colon3\frac{1}{2}=n\colon2 \\ we\text{ can rewrite it as } \\ \frac{2\frac{1}{2}}{3\frac{1}{2}}=\frac{n}{2\text{ }} \\ In\text{ this form we can easily se}e\text{ that in order to solve for n , we just have to multiply both sides of the equation by 2} \\ 2\cdot\mleft\lbrace\frac{2\frac{1}{2}}{3\frac{1}{2}}=\frac{n}{2\text{ }}\mright\rbrace\cdot2 \\ =\frac{2\cdot2\frac{1}{2}}{3\frac{1}{2}}=n \\ n=\frac{2\cdot2\frac{1}{2}}{3\frac{1}{2}}=\frac{5}{3\frac{1}{2}}=\frac{5}{\frac{7}{2}}=5\cdot\frac{2}{7}=\frac{10}{7} \\ \\ \end{gathered}[/tex][tex]2\frac{1}{2}\colon3\frac{1}{2}=n\colon2[/tex]we can rewrite the expression as :
[tex]\frac{2\frac{1}{2}}{3\frac{1}{2}}=\frac{n}{2\text{ }}[/tex]Now we can see easily that that in order to solve for n , we just have to multiply both sides of the equation by 2
[tex]2\cdot\lbrace\frac{2\frac{1}{2}}{3\frac{1}{2}}=\frac{n}{2\text{ }}\rbrace\cdot2[/tex][tex]=\frac{2\cdot2\frac{1}{2}}{3\frac{1}{2}}=n[/tex][tex]n=\frac{2\cdot2\frac{1}{2}}{3\frac{1}{2}}=\frac{5}{3\frac{1}{2}}=\frac{5}{\frac{7}{2}}=5\cdot\frac{2}{7}=\frac{10}{7}[/tex]5) Select all the expressions that equal 3^4. (a) 7 (b) 413 (c) 12 (d) 81 (e) 64 (f) 9^2.
Answer:
(d) 81 (f) 9^2.
Explanation:
Given the expression:
[tex]3^4[/tex]We can write its equivalent form as:
[tex]\begin{gathered} 3^4=3\times3\times3\times3 \\ =81 \\ 3^4=(3^2)^2=9^2 \end{gathered}[/tex]The correct choices are D and F.
To calculate the cost of painting his silo, a farmer must find its height. The farmer uses a cardboard square to line up the topand bottom of the silo as shown in the diagram below. Approximate the height of the silo, rounded to the nearest foot.6 ftfeet10 ft
Given:
A figure with measurement is given.
Required:
Find the height of the silo.
Explanation:
The given figure is:
Use the geometric man theorem in the right triangle ABD.
[tex]\begin{gathered} \frac{AC}{BC}=\frac{CD}{AC} \\ AC^2=BC\times CD \end{gathered}[/tex][tex]\begin{gathered} CD=BD-BC \\ =BD-6 \end{gathered}[/tex]Substitute the given values.
[tex]\begin{gathered} (10)^2=6\times(BD-6) \\ 100=6(BD-6) \\ (BD-6)=\frac{100}{6} \\ (BD-6)=\frac{50}{3} \end{gathered}[/tex][tex]\begin{gathered} BD=\frac{50}{3}+6 \\ =\frac{50+18}{3} \\ =\frac{68}{3} \\ =22.7\text{ ft} \\ \approx23\text{ ft} \end{gathered}[/tex]Final Answer:
The height of the silo is approximately 23 ft.
what is the range of set of the data in the table
The range is calculated by subtracting the lowest value from the highest value. So:
[tex]\begin{gathered} R=16-6 \\ R=10 \end{gathered}[/tex]complete the following deductive proof of the triangle angle sum theorem
The triangle angle sum theorem states that sumof interior angles in a triangle equals 180 degrees.
Here the interior angles are ∠3, ∠4, and ∠5.
To prove that m∠3 + m∠4 + m∠5 = 180 degrees, we have the following:
∠1 and ∠2 and ∠3 from line CP: Definition of a straight angle
m∠1 + m∠2 + m∠3 = 180 degrees: Substitution
Line CP is parallel to line AB: Given
∠1 ≅ ∠4, ∠2 ≅ ∠5: If two parallel lines are cut by a transversal, alternate interior angles are congruent.
m∠1 = m∠4, m∠2 = m∠5: Definition of congruence
m∠4 + m∠5 + m∠3: = 180 degrees: Commutative property
m∠3 + m∠4 + m∠5 = 180 degrees: Angle Addition Postulate
Which points are reflections of each other across the y-axis? 8 RI NOW 2 $ y WINE LAR 07.3) and (7. -3) O (-5, 4) and (5, 4) She (1, -8) and (1,87
the answer is (-7, -3) and (7, -3)
Use the side-splitter theorem to solve for x in the triangle below. 5 х 24 10
The side splitter theorem states that if a line intersects two sides of a triangle and is parallel to the third side of the triangle, it divides those two sides proportionally.
So:
x/24 = 5/10
Solve the proportion for x:
10x =24 (5)
10x = 120
x= 120/10
x= 12
find the present value for the following future amount $9780 at 2.5% compounded semiannually for 11 years (do not round until the final answer. then round to the nearest cent as needed)
The compound interest formula is given by:
[tex]A=P(1+\frac{r}{n})^{nt}[/tex]where P is the principal (the initial value), r is the interest rate in decimal form, n is the number of times the interest is compounded in a given time t.
In this case we know that the future amount is 9780, this means that A=9780. Furthermore, we know that r=0.025, n=2 (since the interest is compounded semiannually) and t=11. Pluging this values in the formula a solving for P, we have:
[tex]\begin{gathered} 9780=P(1+\frac{0.025}{2})^{2\cdot11} \\ P=\frac{9780}{(1+\frac{0.025}{2})^{2\cdot11}} \\ P=7441.29 \end{gathered}[/tex]Therefore, the present value of our investment is $7441.29.
A certain plant grows 1 3/4 inches every week. How long will it take the plant to grow 7 3/4 inches?
Firsr, we must convert the mixed fractions to simple fractions in order to solve this question:
[tex]1\text{ }\frac{3}{4}=\frac{4\cdot1+3}{4}=\frac{7}{4}[/tex]and
[tex]7\frac{3}{4}=\frac{4\cdot7+3}{4}=\frac{31}{4}[/tex]Now, we can solve this question by means of the rule of three:
[tex]\begin{gathered} \frac{7}{4}\text{inches ------- 1 we}ek \\ \frac{31}{4}\text{inches ------- x} \end{gathered}[/tex]hence,
[tex]\begin{gathered} x=\frac{\frac{31}{4}\cdot1}{\frac{7}{4}} \\ x=\frac{\frac{31}{4}}{\frac{7}{4}} \end{gathered}[/tex]by applying the Sandwich law, we have
[tex]\begin{gathered} x=\frac{31\cdot4}{7\cdot4} \\ x=\frac{31}{7} \end{gathered}[/tex]In mixed fraction, 31/7 is
[tex]4\frac{3}{7}[/tex]that is, 4 and 3/7 weeks
factor this polynomial completely[tex] {x}^{2} - x - 20[/tex]
Explanation
Given the expression
[tex]x^2-x-20[/tex]Therefore;
[tex]\begin{gathered} x^2-x-20 \\ =x^2-5x+4x-20 \\ =x(x-5)+4(x-5) \\ =(x+4)(x-5) \end{gathered}[/tex]Answer:
[tex](x+4)(x-5)[/tex]What is the solution to the system of equations in the graph?A. There are no solutionsB. There are infinitely many solutionsC. (3, 7)D. (7, 3)
Given the system of equations in the graph below:
[tex]\begin{bmatrix}x+y=3 \\ x+y=7\end{bmatrix}[/tex]Isolate x for : x+y=3
[tex]y=3-x[/tex]substitue y = 3 - x
[tex]\begin{gathered} \begin{bmatrix}3-y+y=7\end{bmatrix} \\ 3=7 \end{gathered}[/tex]Therefore there are no solutions:
Hence the correct answer is Option A
Find the assessed value of a home with a market value of $88,000 if theassessment rate is 42%.
Given that the Assessment rate = 42%
Market value = $ 88,000
To get the assessed value, we will find 42% of $ 88, 000
[tex]\begin{gathered} \frac{42}{100}\text{ x \$ 88, 000} \\ \\ \frac{3696000}{100} \\ \\ =\text{ \$ 36,960} \end{gathered}[/tex]Assessed value = $ 36,960
A potter use 3/5 of pound of clay to make a bowl. How many bowls could potter make 10 pound of clay?
Let x be the number of bowls the potter could make 10 pound of clay
3/5 pound= 1 bowl
10 pound = x
cross-multiply
[tex]\frac{3}{5}x=10[/tex]Multiply both-side of the equation by 5/3
[tex]x=10\times\frac{5}{3}[/tex][tex]=\frac{50}{3}[/tex][tex]=16\text{ }\frac{2}{3}[/tex]= DATA ANALYSIS AND STATISTICS Interpreting a bar graph A local real estate company has 6 real estate agents. The number of houses that each agent sold last year is shown in the bar graph below. Use this bar graph to answer the questions. Number of Houses Sold 12 10 8 6 4 Alonzo Greg Yolanda Agent Ashley Deshaun Carmen (a) Which agent sold the fewest houses? Alonzo Greg O Yolanda How many houses did that agent sell? 2 house(s) O Ashley (b) How many more houses did Alonzo sell than Greg? more house(s) (c) How many agents sold at least 7 houses? agent(s) Deshaun X O Carmen ? $0/5 ^ NIKI
Step 1
Given;
Step 2
A)
[tex]\begin{gathered} The\text{ agent that sold the fewest houses is Yolando} \\ Yolanda\text{ sold 2 houses} \end{gathered}[/tex]B)
[tex]\begin{gathered} Greg\text{ sold 7 houses} \\ Alonzo\text{ sold 11 house} \\ 11-7=4 \\ Thus\text{ 4 more houses} \end{gathered}[/tex]C)
[tex]\begin{gathered} Alonzo,Greg\text{ and Carmen sold at least 7 houses} \\ Thus\text{ 3 agents sold at least 7 houses} \end{gathered}[/tex]Answer;
A) Yolanda. Yolanda sold 2 houses
B) Alonzo sold 4 more houses than Greg
C) 3 agents sold at least 7 houses
Determine whether the information in each table is linear. If so find the constant rate of change. If not explain your reasoning..
EXPLANATION
Since we have the table with the values of x and y, we can draw the graph as show as follows:
The rate of change can be computed by taking two given points and calculating the slope as shown as follows:
[tex]\text{Slope}=\frac{y_2-y_1}{x_2-x_1}[/tex]As we have (x_1,y_1) = (1,13) and (x_2,y_2) = (3,39), substituting terms:
[tex]\text{Slope}=\frac{39-13}{3-1}[/tex]Subtracting numbers:
[tex]Slope=\frac{26}{2}[/tex]Simplifying:
[tex]\text{Slope}=rate_{\text{ }}of_{\text{ }}change=13[/tex]The constant rate of change is 13
The function is linear because we have a constant rate of change and the form of the graph is a line.
New machine has productivity (measured in the number of product details) 12% greater than the last model . After replacing the machines during renovation ,a plant has 5% fewer models than it had old models before. By what percent did the number of product details on this plant change?
Solution
Let x the original productivity
With the first case the new productivity would be:
1.12 x
After the second case the new productivity is given by:
(1-0.05)* 1.12x = 1.064x
Then the increase can be founded on tihis way:
[tex]\frac{1.064x}{x}\cdot100=6.4[/tex]the number of product details on this plant change by 6.4%
What is the formula of this formula of this sequence? 8; 4; 2; 1; 1/2; 1/4; 1/8; 1/16
The sequence is a Geometric Sequence.
The formula of a geometric sequence is given to be:
[tex]a_n=a_1r^{n-1}[/tex]where a₁ is the first term of the sequence, and r is the common ratio.
The common ratio is calculated to be:
[tex]\begin{gathered} r=\frac{a_2}{a_1}=\frac{4}{8} \\ r=\frac{1}{2} \end{gathered}[/tex]and the first term is:
[tex]a_1=8[/tex]Therefore, the formula for the nth term is given to be:
[tex]a_n=8(\frac{1}{2})^{n-1}[/tex]using the standard form, (MATH PROBLEM) of the group given quadratic equation, factor the left hand side of the equation into two linear factors
Factors are (6x-5) and (7x+1).
Given:
The quadratic equation is
[tex]42x^2=29x+5[/tex]The objective is to factor the equation.
The quadratic equation can be written as,
[tex]\begin{gathered} 42x^2=29x+5 \\ 42x^2-29x-5=0 \end{gathered}[/tex]On factorizing the above equation,
[tex]\begin{gathered} 42x^2+6x-35x-5=0 \\ 6x(7x+1)-5(7x+1)=0 \\ (6x-5)(7x+1)=0 \end{gathered}[/tex]Hence, the factors are (6x-5)(7x+1)=0.
Find fractional notation 55%
55% means 55 out of every 100.
This as a fraction would mean:
[tex]\frac{55}{100}[/tex]Simplifying,
[tex]\frac{55}{100}\rightarrow\frac{55\div5}{100\div5}\rightarrow\frac{11}{20}[/tex]We get that 55% as a fraction is 11/20
what is the distance formula between (7,11) and (-1,5)
Let's begin by listing out the information given to us:
[tex]\begin{gathered} (x_{1,}y_1)=(7,11) \\ (x_{2,}y_2)=(-1,5) \end{gathered}[/tex]The distance formula is given by the Pythagoras theorem shown below:
[tex]\begin{gathered} d=\sqrt[]{(x_2-x_1)^2+(y_2-y_1)^2} \\ d=\sqrt[]{(-1-7)^2+(5-11)^2}=\sqrt[]{(-6)^2+(-6)^2} \\ d=\sqrt[]{36+36}=\sqrt[]{72} \\ d=6\sqrt[]{2} \end{gathered}[/tex]OR
The distance formula is the difference between two points on the same coordinate, all squared
d
A tank is full and holds 600 gallons of water. It is being pumped out at a rate of 30 gallons per hour. Let y be the number of gallons in the tank. Is it discrete or continuous? And what are they domain and range?
The volume of water in the tank can be expressed by the equation below:
[tex]y(t)\text{ = 600-30}\cdot t[/tex]Where y is the volume of the tank and t is the time elapsed since the tank started pumping water out.
A function is continuous when it is difined for all the values inside its domain. The domain of this function is all the positive real numbers, this is because the input represents time and there isn't negative time. For each fraction of hour there will be an associated volume of water in the tank, therefore the function is continuous.
The domain of the function is:
[tex](0,\infty([/tex]The range of the function is the set of values that it can output for the given domain. In this case the maximum value of the function is the total capacity of the tank 600 gallons, while the minimum value happens when the tank is empty, so the range is:
[tex](0,600)[/tex]Explain the pattern in the simplification of imaginary numbersi, i, i, i*,Edit View Insert Format Tools Table12ptParagraph ✓ BIUA Qv T²v**
Given:
[tex]i^2,i^2,i^3,i^^4,...[/tex]Required:
We need to explain the pattern
Explanation:
[tex]\begin{gathered} i^1=i \\ i^2=-1 \\ i^3=-i \\ i^4=1 \\ i^5=i^4*i=1*i=i \\ i^6=i^4*i^2=1*-1=-1 \\ i^7=i^4*i^3=1*-i=-i \\ i^8=i^4*i^4=1*1=1 \\ . \\ . \\ . \end{gathered}[/tex]As we can see that
the values of
[tex]i^{4n+1}[/tex]are equal where n is set of real numbers
similarly for
[tex]i^{4n+2}[/tex]also for
[tex]i^{4n+3}[/tex]and for
[tex]i^{4n+4}[/tex]where all n are from the set of real numbers