ANSWER
x(12 + 32)
EXPLANATION
Let x be 'the number'.
A number times... means 'a number multiplied by...'
The sum of 12 and 32 is (12 + 32)
The complete algebraic expression is x(12 + 32)
Sally has a mass of 70 kg and dave weighs 170 pounds what is Sally weight as a percentage of Dave’s weight
The percentage is 91% approx.
We have to find percentage here.
A percentage is a figure or ratio stated as a fraction of 100 in mathematics. Although the abbreviations "pct.", "pct.", and occasionally "pc" are also used, the percent symbol, "%," is frequently used to indicate it. A % is a number without dimensions and without a standard measurement.
To find percentage, we need to have both the terms in the same unit.
So, we will convert kg into pounds
1 kg = 2.205 pounds
70 kg = 2.205 * 70 = 154.35 pounds
Sally's weight = 154.35 pounds
Dave's weight = 170 pounds
Percentage = Sally's weight/ Dave's weight * 100
= 154.35/170 * 100
= 90.794%
= 91% approx.
The percentage is 91% approx.
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Could you help me with this problem?There are 7 acts in a talent show.A comedian, a guitarist, a magician, a pianist, a singer, a violinist, and a whistler.A talent show host randomly schedules the 7 acts.Compute the probability of each of the following events.Event A: The magician is first, the comedian is second, and the whistler is third.Event B: The first three acts are the guitarist, the pianist, and the singer, in any order.Write your answers as fractions in simplest form.
EXPLANATION
For the event B, the order of the first 3 acts doesn't matter.
So, the number of acts taken from the seven acts when the order doesn't matter is calculated using combinations.
[tex]C(m,n)=\frac{m!}{n!(m-n)!}[/tex][tex]C(7,3)=\frac{7!}{3!(7-3)!}=\frac{7!}{3!4!}[/tex]Computing the factorials:
[tex]C(7,3)=\frac{5040}{6\cdot24}=\frac{5040}{144}=35[/tex]Hence, the number of ways the three acts could be given are 1:C(7,3)
Therefore, the probability of the event B is:
[tex]P(B)=\frac{1}{35}[/tex]For the event A, the order matters, so the difference between combinations and permutations is ordering. When the order matters we need to use permutations.
The number of ways in which four acts can be scheculed when the order matters is:
[tex]P(m,n)=\frac{m!}{(m-n)!}[/tex][tex]P(m,n)=\frac{7!}{(7-3)!}=\frac{5040}{24}=210[/tex]The number of ways the magician is first, the comedian is second and the whistler is third are 1:P(7,4)
Therefore, the probability of the event A is.
[tex]P(A)=\frac{1}{210}[/tex]Which of the following is a factor of the polynomial Step By Step Explanation Please
Use the quadratic formula.
[tex]x=\frac{-b\pm\sqrt[]{b^2-4ac}}{2a}[/tex]Where a = 3, b = -31, and c = -60.
[tex]x=\frac{-(-31)\pm\sqrt[]{(-31)^2-4(3)(-60)}}{2(3)}[/tex]Solve to find both solutions.
[tex]x=\frac{31\pm\sqrt[]{961+720}}{6}=\frac{31\pm\sqrt[]{1681}}{6}=\frac{31\pm41}{6}[/tex]Rewrite the expression as two.
[tex]\begin{gathered} x_1=\frac{31+41}{6}=\frac{72}{6}=12 \\ x_2=\frac{31-41}{6}=\frac{-10}{6}=-\frac{5}{3} \end{gathered}[/tex]Once we have the solutions, we express them as factors. To do that, we have to move the constant to the right side of each equation.
[tex]\begin{gathered} x=12\to(x-12) \\ x=-\frac{5}{3}\to(3x+5)_{} \end{gathered}[/tex]As can observe, the factor of the polynomial is (x-12).
Therefore, the answer is d.Determine the solution to the system of equations using substitution. (1 pt)2:+ y=6y = -6(2,6)(2,-6)(4, -2)(-2,4)
2x + y = 6 (1)
y = x - 6 (2)
Substituting y in equation (1)
2x + x - 6 = 6
3x - 6 = 6 Isolating 3x
3x = 6 + 6
3x = 12 Isolating x
x = 12/3 = 4
If x is 4 , then y is equal to -2 ( from equation (2) y)
# 3 symbols of inequalities and the coordinate system...hello I'm a 7th grader can u please help me with my math summer package and explain it in a way that a 7th grader can understand it
Given: A grocery store is located at the origin (0,0). Madison lives 3 blocks west of the grocery store, and Gavin lives 5 blocks west of the grocery store.
Required: To determine the coordinates of Madison's house and Gavin's house and the distance between the grocery store and madison's and Gavin's house. Also, write inequalities for the distance.
Explanation: Let the graph represents the directions as follows-
Then, the direction west lies on the negative x-axis. So, according to the question, Madison lives 3 blocks west of the grocery store, and Gavin lives 5 blocks west of the grocery store. This can be represented as follows-
Here, M represents Madison's house, and G represents Gavin's house. Now the distance from the grocery store to Madison's house is 3 blocks and to Gavin's house is 5 blocks.
Gavin lives at a greater distance from the store. Let d(M) represent the distance of Madison's house from the store and d(G) represent the distance of Gavin's house from the store. Then-
[tex]\begin{gathered} 0Final Answer: Coordinates of Madison's house=(0,-3).Coordinate of Gavin's house=(0,-5)
Distance from the grocery store to Madison's house=3 unit blocks.
Distance from the grocery store to Gavin's house=5 unit blocks.
Inequalities are-
[tex]\begin{gathered} 0\lt d(M))\leqslant3 \\ 0\lt d(G))\leqslant5 \end{gathered}[/tex]The side of a square lot is (5×-3) meters. How many meters of fencing materials are needed to enclose the square lot?
The length of the fencing will be the perimeter of the given square with side (5x - 3) thus (20x - 12) meters will be the fencing length.
What is a square?A square is a geometrical figure in which we have four sides each side must be equal and the angle between two adjacent sides must be 90 degrees.
As per the given,
Side of square = 5x - 3
The fencing around the square will cover the complete perimeter of the square.
Since the perimeter of the square = 4 × side
Therefore,
Length of fencing = 4 × (5x - 3)
Length of fencing = 20x - 12
Hence "The length of the fencing will be the perimeter of the given square with side (5x - 3) thus (20x - 12) meters will be the fencing length".
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A company needs to take 10 sample sensor readings if the sensor collects data at 1/3 of a sample per second how long will it take the company to take all 10 samples
Given:
Sample space = 10
Rate = 1/3 per second
$75 dinner, 6.25% tax, 18% tip please show work.You have to find the total cost
According the the information given in the exercise, you know that the cost of the dinner was:
[tex]d=_{}$75$[/tex]Where "d" is the cost of the dinner in dollars.
Convert from percentages to decimal numbers by dividing them by 100:
1. 6.25% tax in decimal for:
[tex]\begin{gathered} tax=\frac{6.25}{100} \\ tax=0.0625 \\ \end{gathered}[/tex]2. 18% tip in decimal form:
[tex]\begin{gathered} tip=\frac{18}{100} \\ \\ tip=0.18 \end{gathered}[/tex]To find the amount in dollars of the tax and the the amount in dollars of the tip, multiply "d" by the decimals found above.
Knowing the above, let be "t" the total cost in dollars.
This is:
[tex]\begin{gathered} t=d+0.0625d+0.18d \\ t=75+(0.0625)(75)+(0.18)(75) \\ t=93.1875 \end{gathered}[/tex]Therefore the answer is: The total cost is $93.1875
Please see image attached. I am not able to solve, even after using the formula
Given:
Total number of cub scouts is 20 and the number of scout is 10 more than 2 times the number of adult leaders.
Required:
We need to find the number of adult leaders.
Explanation:
Lets consider cub scouts as c and adult leaders as a so the
[tex]c=20[/tex]and the formula for adult is
[tex]\begin{gathered} c=2a+10 \\ 20=2a+10 \end{gathered}[/tex]simplify as:
[tex]\begin{gathered} 10=2a \\ a=5 \end{gathered}[/tex]Final answer:
Number of adult leaders is 5
Use the distributive property to simplify 10 - 5( -3-7m) completely .
Simplify the expression by using the distributive property.
[tex]\begin{gathered} 10-5(-3-7m)=10+(-5)\cdot(-3)+(-5)\cdot(-7m) \\ =10+15+35m \\ =25+35m \end{gathered}[/tex]So answer is 25 + 35m.
Find the value of f(-9).
The function f(-9) is the -x value, find where the line is in the -y direction at -x = -9. The line crosses -y = -3 at -x = -9.
What is meant by the graph?In mathematics, a graph is a visual representation or diagram that shows facts or values in an ordered way. The relationships between two or more items are frequently represented by the points on a graph.
In discrete mathematics, a graph is made up of vertices—a collection of points—and edges—the lines connecting those vertices. In addition to linked and disconnected graphs, weighted graphs, bipartite graphs, directed and undirected graphs, and simple graphs, there are many other forms of graphs. A graph is a diagram that depicts the connections between two or more objects.
The function f(-9) is the -x value, find where the line is in the -y direction at -x = -9. The line crosses -y = -3 at -x = -9.
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a blu ray player costs $80.99 in the store. what would your total cost be if the sales tax is 5.5%
ANSWER:
$ 85.44
STEP-BY-STEP EXPLANATION:
We have the value after tax, we must calculate the sum between the original value and the value equivalent to the established percentage, therefore, we calculate it like this:
[tex]\begin{gathered} p=80.99+80.99\cdot\frac{5.5}{100} \\ p=80.99+4.45 \\ p=\text{ \$85.44} \end{gathered}[/tex]The final price is $ 85.44
Help solving rational equations by cancelling denominator
A linear regression model for the revenue data for a company is R=25.9t + 204 where R is total annual revenue and t is time since 1/31/02 in years.
The linear regression model is
[tex]R=25.9t+204[/tex]Where
R is the total annual revenue (dependant variable)
t is the time, in years, since 1/31/02 (independent variable)
To predict the annual revenue for the period ending 1/31/10, the first step is to determine the value of t. Considering that t=0 is the first recorded year (1/31/02), the value of t corresponding to period 1/31/10 is the number of years passed since, including 2002, which is 9 years.
So you have to calculate R for t=9. Replace the formula with t=9 and calculate the corresponding value of R
[tex]\begin{gathered} R=25.9\cdot9+204 \\ R=437.1 \end{gathered}[/tex]R≈437 billion dollars
Please help meSolve using A=PertThe half life gets me each time.
Solve the inequality. Express your answer using set notation or interval notation. Graph the solution set.
Answer:
(D) {xIx ≥ 5} or [5, ∞)
Explanation:
Given inequality: 5x - 11 ≥ 9 + x
By collecting the like terms, we have
5x - x ≥ 9 + 11
4x ≥ 20
Divide bothsides by 4
4x/4 ≥ 20/4
x ≥ 5
In set notation, we have {5, ∞}
The graph of the solution set is
Which expression would be easier to simplify if you used the associativeproperty to change the grouping?
In option A, if expression is simplify with out using associative property then addition of 4/9 and -2/9 is easy, as compare to addition 6 and 4/9. So no need to apply associateive property to option A.
In option B, 60 and 40 can be easily add as compare to 40 and -27 so this expression do not need to apply associative property.
In option C, the expression is easier to simplify if 5/2 and -1/2 is added, which is possible if associative is apply to the expression.
[tex]\begin{gathered} (2+\frac{5}{2})+(-\frac{1}{2})=2+(\frac{5}{2}-\frac{1}{2}) \\ =2+(\frac{5-1}{2}) \\ =2+2 \\ =4 \end{gathered}[/tex]Thus option C use associative property to make the simplification easier.
Answer: Option C.
In the lab, Deandre has two solutions that contain alcohol and is mixing them with each other. Solution A is 10% alcohol and Solution B is 60% alcohol. He uses200 milliliters of Solution A. How many milliliters of Solution B does he use, if the resulting mixture is a 40% alcohol solution?
The percentage of alcohol of a solution i is given by the quotient:
[tex]p_i=\frac{v_i}{V_i},_{}[/tex]where v_i is the volume of alcohol in the solution i and V_i is the volume of the solution i.
From the statement of the problem we know that:
1) Solution A has 10% of alcohol, i.e.
[tex]p_A=\frac{v_A_{}}{V_A}=0.1.\Rightarrow v_A=0.1\cdot V_A.[/tex]2) Solution B has 60% of alcohol, i.e.
[tex]p_B=\frac{v_B}{V_B}=0.6\Rightarrow v_B=0.6\cdot V_B.[/tex]3) The volume of solution A is V_A = 200ml.
4) The resulting mixture must have a percentage of 40% of alcohol, so we have that:
[tex]p_M=\frac{v_M}{V_M}=0.4.[/tex]5) The volume of the mixture v_M is equal to the sum of the volumes of alcohol in each solution:
[tex]v_M=v_A+v_{B\text{.}}_{}[/tex]6) The volume of the mixtureVv_M is equal to the sum of the volumes of each solution:
[tex]V_M=V_A+V_B\text{.}[/tex]7) Replacing 5) and 6) in 4) we have:
[tex]\frac{v_A+v_B}{V_A+V_B_{}}=0.4_{}\text{.}[/tex]8) Replacing 1) and 2) in 7) we have:
[tex]\frac{0.1\cdot V_B+0.6\cdot V_B}{V_A+V_B}=0.4_{}\text{.}[/tex]9) Replacing 3) in 8) we have:
[tex]\frac{0.1\cdot200ml_{}+0.6\cdot V_B}{200ml_{}+V_B}=0.4_{}\text{.}[/tex]Now we solve the last equation for V_B:
[tex]\begin{gathered} \frac{0.1\cdot200ml+0.6\cdot V_B}{200ml_{}+V_B}=0.4_{}, \\ \frac{20ml+0.6\cdot V_B}{200ml_{}+V_B}=0.4_{}, \\ 20ml+0.6\cdot V_B=0.4_{}\cdot(200ml+V_B), \\ 20ml+0.6\cdot V_B=80ml+0.4\cdot V_B, \\ 0.6\cdot V_B-0.4\cdot V_B=80ml-20ml, \\ 0.2\cdot V_B=60ml, \\ V_B=\frac{60}{0.2}\cdot ml=300ml. \end{gathered}[/tex]We must use 300ml of Solution B to have a 40% alcohol solution as the resulting mixture.
Answer: 300ml of Solution B.
60 went into a machine and 72 came out.What percent increase did this machine use?
From this question, we can deduce he following:
Original value = 60
New value = 72
Let's find the percentage increase.
To find the percentage increase, apply the formula below:
[tex]\text{ Percent increase = }\frac{New\text{ value - old value}}{old\text{ value}}\ast100[/tex]Thus, we have:
[tex]\begin{gathered} \text{Percent increase = }\frac{72-60}{60}\ast100 \\ \\ \text{Percent increase = }\frac{12}{60}\ast100 \\ \\ \text{Percent increase = }0.2\ast100 \\ \\ \text{Percent increase = 20 \%} \end{gathered}[/tex]Therefore, the percent increase is 20%.
ANSWER:
20%
Write the trig equation needed to solve for X. Then solve for X. Round answers to the nearest tenth.
In order to solve for x, we need to use the tangent relation of the angle 48°.
The tangent relation is equal to the length of the opposite leg to the angle over the length of the adjacent leg to the angle.
So we have:
[tex]\begin{gathered} \tan (48\degree)=\frac{x}{17} \\ 1.1106=\frac{x}{17} \\ x=1.1106\cdot17 \\ x=18.88 \end{gathered}[/tex]Rounding to the nearest tenth, we have x = 18.9.
I need help for problem number 9. On the right side of the paper.
Constant of variation ( k ):
• y = 2/3
,• x = 1/4
[tex]k=\frac{y}{x}=\frac{\frac{2}{3}}{\frac{1}{4}}=\frac{8}{3}[/tex]k = 8/3
Based on k we can find the value of y when x =3/4 as follows:
[tex]\begin{gathered} k=\frac{y}{x} \\ y=k\cdot x \\ y=\frac{8}{3}\cdot\frac{3}{4}=2 \end{gathered}[/tex]Answer:
• k = 8/3
,• When ,x, = ,3/4,,, y = 2
Mrs. Brown is putting different colored sand into cups for her 4 daughters to make sand art bottles. The total amount of each color she has is shown in the table. Sand Color Weight (lb) Blue 1516 Pink 34 Purple 12 Turquoise 78 If each color is divided equally among the daughters, how much more pink sand will be available for each girl than purple sand? Write in simplest fraction form
Answer:
11/2 lb
Step-by-step explanation:
If 34 lb of pink sand and 12 lb of purple sand are equally divided among 4 daughters, you want to know how much more pink sand each girl receives.
DifferenceThe difference in amounts seen by each daughter will be ...
difference in amounts / number of daughters = (34 lb -12 lb)/(4 daughters)
= 22/4 lb/daughter = 11/2 lb/daughter
Each girl will have 11/2 more pounds of pink sand than purple sand.
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A sample of 7 adult elephants had an average weight of 12,572 pounds. The standard deviation for the sample was 26 pounds. Find the 95% confidence interval of the population mean for the weights of adult elephants. Assume the variable is normally distributed. Round intermediate answers to at least three decimal places. Round your final answers to the nearest whole number.
Answer
[tex]CI=(12553<\mu<12591)[/tex]Explanation
The confidence interval formula is given by
[tex]\begin{gathered} CI=\bar{x}\pm z\frac{s}{\sqrt[]{n}} \\ \text{Where;} \\ CI\text{ is the 95 percent confidence interval} \\ \bar{x}\text{ is the average weight }=12572 \\ z\text{ is the confidence value }=1.96 \\ s\text{ is the sample standard deviation }=26 \\ n\text{ is the sample size }=7 \end{gathered}[/tex]This implies that
[tex]\begin{gathered} CI=12572\pm1.96(\frac{26}{\sqrt[]{7}}) \\ CI=12572\pm\frac{50.960}{2.646} \\ CI=12572\pm19.259 \\ CI=(12552.741,12591.259) \\ CI=(12553<\mu<12591) \end{gathered}[/tex]The 95% confidence interval of the population mean for the weights of adult elephants is (12553 < μ < 12591)
In the expression 9+2z what is the variable?
To answer this question, we will define some things first.
For every mathematical expression or term, it consist of three parts:
1) Coefficient
2) Variable: a symbol that stands in for an unknown value in a mathematical expression
3) Constant
In the expression given:
[tex]\begin{gathered} 9+2z \\ 9\text{ is the constant} \\ 2\text{ is the coefficient} \\ z\text{ is the variable} \end{gathered}[/tex]So the variable in the expression is z.
Which answer choice shows 3.002 written in expanded form?A) 3 + 0.2B) 3 + 0.02C) 3 + 0.002D) 3+ 0.0002
SOLUTION
We want to know which answer choice shows 3.002 written in expanded form
To do this let us subtract 3.002 from 3, we have
We got 0.002
So the expanded form is
[tex]3+0.002[/tex]Hence the correct answer is option C
72, - 16, - 8, 40
[tex]72, - 16, - 8, 40[/tex]
The solution to the mathematical problem is using the mathematical operation of addition, getting the sum of the numbers as 88.
What is an addition operation?An addition operation is one of the four basic mathematical operations, including division, subtraction, and multiplication.
When a number is added to another, the result of the addition operation is a sum or the total.
Addition operations are classified into two or more addends, the plus symbol (+), the equal sign (=), and the sum.
72 + -16 + -8 + 40
Group additions and subtractions:
72 + 40 + -16 + -8
Simplify the operations:
= 112 - 24
Solution:
= 88
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Miss Taylor drove 30 miles in March she drove 9 times as many miles in May as she did in March she drove 2 times as many miles in April as she did in May how many miles did Miss Taylor Drive in April.
then we use the statement to solve
Miss Taylor drove 30 miles in March
[tex]March=30[/tex]she drove 9 times as many miles in May as she did in March
[tex]\begin{gathered} May=9\text{March} \\ May=9\times30=270 \end{gathered}[/tex]she drove 2 times as many miles in April as she did in May
[tex]\begin{gathered} April=2May \\ April=2\times270=540 \end{gathered}[/tex]Taylor Drove 540 Miles in April
May I please get help with this. I need help with finding the original and final points on the figure and also finding out where I should put my reflection?
Answer:
Step-by-step explanation:
The rule for a reflection over the y-axis is represented by the following equation:
[tex](x,y)\rightarrow(-x,y)_{}[/tex]Therefore, for the given figure and given point:
What is the image point of (1,−3) after a translation right 2 units and up 2 units?
For this problem we have the following point given:
[tex]P=(1,-3)[/tex]And we want to determine the image point after a translation of 2 units to the right and upward. So then we just need to do the following:
[tex]I=(1+2,-3+2)[/tex]And after do the math we got:
[tex]I=(3,-1)[/tex]And the final answer for this case would be I=(3,-1)
Correctz is jointly proportional to x and y. If z = 115 when x = 8 and y = 3, find z when x = 5 and y = 2. (Round off your answer to the nearest hundredth.)
When we have a number that is jointly proportional to two other numebrs, the formula is:
[tex]a=kcb[/tex]This means "a is jointly proportional to c and b with a factor of k"
Then, we need to find the factor k.
In this case z is jointly proportional to x² and y³
This is:
[tex]z=kx^2y^3[/tex]Then, we know that z = 115 when x = 8 and y = 3. We can write:
[tex]115=k\cdot8^2\cdot3^3[/tex]And solve:
[tex]\begin{gathered} 115=k\cdot64\cdot27 \\ 115=k\cdot1728 \\ k=\frac{115}{1728} \end{gathered}[/tex]NOw we can use k to find the value of z when x = 5 and y = 2
[tex]z=\frac{115}{1728}\cdot5^2\cdot2^3=\frac{115}{1728}\cdot25\cdot8=\frac{2875}{216}\approx13.31[/tex]To the nearest hundreth, the value of z when x = 5 and y = 2 is 13.31